2025 Year 9MAT5 Class
Student name: _______________________
Topic: Area and Surface Area Workbook
Surface area formulas
10.02C Area of composite shapes - worksheet
Understanding
1 Are these statements true or false?
a The area of a composite shape can be found by dividing it into smaller, basic shapes,
finding the area of each of these shapes, and then adding these areas together.
b The area of a composite shape can be found by subtracting the larger shape from the
smaller shape.
c The area of a composite shape is always expressed in square units.
d If a composite shape is made up of two identical rectangles, the total area can be found
by calculating the area of one rectangle and then doubling it.
2
a Name the two geometric shapes that
make up this composite shape.
b Explain how to find the total area.
3
a Name the two geometric shapes that
make up this composite shape.
b Explain how to find the total area.
Fluency
4
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a Find the area of rectangle B.
b Find the total area of the given shape.
5 Find the total area:
a b
c d
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e f
Example 1
6 Find the shaded area:
a b
c d
7 For each of these composite shapes:
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i What basic shapes make up the composite shape?
ii Find the area, rounded to two decimal places.
a b
8 Find the area of the composite shapes. Round your answer to one decimal place.
a b
c d
9 Find the shaded area in the diagrams. Round your answer to one decimal place.
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a b
c d
Example 2
10 Find the shaded area, rounded to two decimal places:
a b
11 Eddie designs a plot of land which contains
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his house and garden.
a Find the total area of the plot of land.
b Find the area of the garden.
Reasoning
12 A rectangle with dimensions width, w, and length, 2w, has a square with side length s cut
out of it.
a Write an expression for the area, A, of the composite shape.
b Does the area change if the position of the square changes?
13 A piece of origami paper, orginally in the
shape of a parallelogram, is folded along its
shortest diagonal.
Explain how to find the total area covered
by the folded paper.
14 Joshua and Lila are calculating the area of a composite shape, that consists of a rectangle
and a semicircle. The rectangle is 10 cm long and 6 cm wide. The diameter of the semicircle
is the same as the width of the rectangle.
Joshua calculates the area of the rectangle and the semicircle separately and then adds
them together. Here's his solution:
1
Area = (10 cm × 6 cm) + ( ) × π × (3 cm)2 = (60 cm2 + 14.13 cm2 )
2
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Lila argues that they can calculate the area of the entire shape as a whole, without
separating the rectangle and the semicircle. She calculates the area as:
(10 cm × 6 cm) + π × (3 cm)2
Which student's approach is correct and why?
15 Ava and Max are calculating the area of a composite shape that consists of a square of side
lengths 5 m and a quarter-circle.
Ava's approach is to calculate the area of the square and the quarter-circle separately. Here's
her calculation:
1
Area = (5 m × 5 m) + ( ) × π × (2.5 m)2 = 29.91 m2
4
However, Max argues that the radius of the quarter-circle should be the same as the side of
the square, and calculates the area of the quarter-circle as:
1
Area = (5 m × 5 m) + × π × (5 m)2 = 44.63 m2
4
Who is correct in this situation and why?
Problem-solving
16 A square has a quarter of a circle attached to one of its sides. The square has side length
9 cm and the quarter of a circle has radius equal to the sides of the square. Find the total
area, rounded to two decimal places.
17 You are tiling a kitchen floor, which has a rectangular shape measuring 4.5 m in length and
3 m in width. Along the edges of the room, there is a border of square tiles, each measuring
15 cm on a side. The remaining interior of the floor will be covered with square tiles
measuring 30 cm on a side. How many of each type of tile are needed?
18 A rectangular park is 30 m wide and 50 m long, inside the park there is a playground area.
The playground consists of a square sandbox with sides measuring 3.2 m and a circular
swing set section with a radius of 3 m.
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a Draw a possible map of the playground.
b What is the area of park excluding the playground areas? Round your answer to two
decimal places.
c The council is going to fertilise the lawn in the park (the area excluding the playground),
for each square metre of lawn they need 250 g of fertiliser. How many kilograms of
fertiliser is needed? Round your answer to two decimal places.
19 The hotel lobby room is to be tiled with
slate tiles as shown. The cost of tiling the
room is $48/m2 .
a Find the area to be tiled.
b How much will it cost to tile the room?
20 The landscaping plan includes a garden
positioned at the top, bordered by a circular
arc and the property boundary.
a Find the area of the lawn in square
metres.
b Find the area of the garden in square
metres. Round your answer to two
decimal places.
c If roll-on lawn costs $12 per square
metre, how much will it cost to cover the
lawn and the garden?
d Find the paved area in square metres.
Round your answer to two decimal
places.
e Paving costs $100 per square metre.
Find the cost to pave the paved area.
21 The pattern for a simple t-shirt features a semicircular neck hole, found in the front piece
only.
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a Find the area of the back of the t-shirt.
b Find the area of the front of the t-shirt, rounded to one decimal place.
c If the front and back pieces are both cut from two rectangular pieces of fabric with
dimensions 90 cm by 80 cm, how much fabric is wasted? Round your answer to the
nearest square centimetre.
d The fabric is 80 cm wide and costs $8 per metre, so one metre of fabric measures 80 cm
by 100 cm. If the t-shirt pieces are cut out of two 0.9 metre lengths, as in part (c), how
much will the fabric cost for 100 t-shirts?
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10.03C Nets of prisms - worksheet
Understanding
1 Are the statements true or false?
a The net of a prism is a two-dimensional representation of the three-dimensional prism.
b A prism can have only one possible net.
c Nets can be used to determine the surface area of a prism.
d A net of a rectangular prism will always have two square faces.
2 In the net of this shape, how many faces
would have a circle cut out of them?
3 How many faces does a rectangular prism have?
Fluency
4 Name these solids:
a b
c d
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5 Which of the following nets fold into a
cube?
A B
C D
6 Which net matches this rectangular prism?
Justify your answer.
A B
C D
7 Name the solid formed by each of these nets:
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a b
c d
Example 1
8 Draw a net for each solid:
a b c d
9 Match each triangular prism with its net.
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a i
b ii
c iii
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d iv
e v
f vi
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g vii
h viii
Reasoning
10 Suppose you are given a net with six congruent square faces. What three-dimensional
shape can you form from it, and how can you prove it?
11 Explain how you could find the surface area of a rectangular prism using the net of a
rectangular prism.
Problem-solving
12 Rose wants to wrap a gift in a box using a
glossy gift wrapper that costs $0.35 per
square metre. How much will Rose pay to
wrap her gift?
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13 U-Pack Moving Company sells two sizes of moving boxes. U-Pack claims to keep their prices
lower than competitors by selling their boxes flat, and having customers assemble the boxes
themselves.
Box 1 sells for $0.02 per square centimetre: Box 2 sells for $0.03 per square centimetre:
a How much will it cost for a customer to buy Box 1?
b How much will it cost for a customer to buy Box 2?
c Which box is cheaper?
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10.04C Surface area of prisms - worksheet
Understanding
1 How many faces does each prism have?
a Rectangular prism b Triangular prism
c Cube d Hexagonal prism
2 Are these statements true or false?
a Surface area can be found by finding the area of the base and multiplying it by the
height.
b The net of a prism can be used to help calculate its surface area.
c A prism is made up of two congruent, parallel, polygonal bases that are connected by
rectangular faces.
d No other face of a prism has the same area as the base.
3 Which net matches this rectangular prism?
A B C D
Fluency
4 The cube has a side length of 6 cm:
a Draw the net.
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b Find the surface area of the cube.
5 Find the surface area:
a b
c d
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e f
6 Find the surface area:
a b
c d
Example 1
7 Find the surface area rounded to two decimal places when necessary.
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a b
c d
8 The figure is a trapezoidal prism.
a Find the value of d rounded to one
decimal place.
b Find its surface area.
Example 2
9 A birthday gift is placed inside the box
shown:
Find the minimum amount of wrapping
paper needed to wrap this gift.
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Example 3
10 Sally is building a storage chest in the shape of a rectangular prism. The chest will be 93 cm
long, 80 cm deep, and 18 cm high. Find the surface area of the chest.
11 The swimming pool has the dimensions
shown.
The sides and base of the pool are to be
tiled. Calculate the area to be tiled,
rounding your answer to two decimal
places.
12 Find the value of x and the surface area of each prism.
a b
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Reasoning
13 If a cube and a rectangular prism have the same volume, will they also have the same
surface area? Justify your answer with an example.
14 John and Ryan are asked to determine the surface area of a rectangular prism with
dimensions 8 units by 5 units by 3 units. Ryan argues that the surface area is 120 square
units, while John believe it's 158 square units. Who is correct and why?
15 A triangular prism and a rectangular prism have the same base area and the same height.
Vlad suggests that they will have the same surface area. Do you agree? Why or why not?
16 Write an expression for the surface area of
this trapezoidal prism. Justify your formula.
Problem-solving
17 A cube has surface area of 1032 cm2 .
a Find the area of one of the square faces.
b Find the length of one side of the cube, rounded to two decimal places.
18 Find the side length of a cube that has a surface area of 726 cm2 .
19 A rectangular box has a surface area of 312 m2 . If width and length of the box are 8 m and
2 m respectively, find the height of the box.
20 Find the surface area of the object shown.
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21 A box that has a rectangular base 2b centimetres in length and 3b centimetres in width. The
height of the box is b centimetres. Calculate the surface area of the box in terms of b.
22 A rectangular prism has a length of 4x metres, width of 3x metres and height of 2x metres. If
the dimensions of this prism are increased by a factor of 2, calculate the increase in the
surface area in terms of x.
23 Dramona is creating a rectangular prism-shaped box with a volume of 360 cm3 . The box must
have a square base, and the height must be twice the length of one side of the base.
Determine the surface area of the box in square centimetres, rounding your answer to one
decimal place.
24 The diagram shows a high rise building.
a Find the surface area of the external
walls of the building.
b If 2% of the surface area is taken up by
metal frames and the rest is glass, how
many square metres of glass are used on
the walls? Round your answer to one
decimal place.
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10.05C Surface area of cylinders - worksheet
Understanding
1 In terms of π and x, find the:
a Circumference of the circle
b Area of the circle
2 Is each statement true or false?
a The surface area of a cylinder includes the area of both bases and the curved surface.
b If you double the radius of a cylinder, the surface area will also double.
c A cylinder that is taller always has a larger surface area than a shorter one.
3 For this cylinder:
a Does this net match the cylinder?
b To find the surface area of the cylinder,
is the radius 8 m and height 4 m?
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Fluency
4 For each pair of cylinders and their nets, find the curved surface area of the cylinder. Round
your answers to two decimal places.
a b
Example 1
5 For each cylinder:
i Find the curved surface area of the cylinder, rounded to two decimal places.
ii Find the total surface area of the cylinder, rounded to two decimal places.
a b
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c d
6 Find the surface area of each cylinder, rounded to two decimal places.
a b
c d
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e f
Example 2
7 The area of the circular face on a cylinder is 225π m2 . The total surface area of the cylinder
is 3210π m2 .
a Find the the radius of the cylinder. b Find the height of the cylinder.
Example 3
8 This cylinder has a surface area of 16 173 m2
:
Find the height the cylinder. Round your
answer to the nearest whole number.
9 This cylinder has a surface area of
54 425 cm2 :
Find the height the cylinder. Round your
answer to the nearest whole number.
10 Find the exact surface area of a cylinder with diameter 6 cm and height 21 cm by leaving
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your answer in terms of π.
11 Find the curved part of a cylinder with a radius of 9.2 m and a height of 15.1 m. Round your
answer to one decimal place.
Reasoning
12 Matea suggests that if the height of a cylinder is doubled then the surface area of the
cylinder will be doubled. Is he correct? Explain your reasoning.
13 Consider a cylinder with a fixed surface area. If you increase the radius of this cylinder, what
will happen to its height? Explain your reasoning.
14 If you have a toilet paper roll (a cylinder) and you want to increase the total amount of paper
on the roll, will it affect the surface area? Justify your answer.
Problem-solving
15 Find the surface area of the figure, rounded
to two decimal places.
16 A cylindrical can of radius 7 cm and height 10 cm is open at one end. Find the external
surface area of the can. Round your answer to two decimal places.
17 Paul is using a toilet paper roll for crafts. He
has measured the toilet paper roll to have a
diameter 4 cm and a length 10 cm.
Find the surface area of the toilet paper roll.
Round your answer to two decimal places.
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18 A paint roller is cylindrical in shape. It has a
diameter of 6.2 cm and a width of 38.1 cm.
Find the area painted by the roller when it
makes one revolution. Round your answer
to two decimal places.
19 The diagram shows a water trough in the
shape of a half cylinder.
Find the exact surface area of the outside of
this water trough, leaving your answer in
terms of π.
20 Amy and Vincent each have a cylinder. Amy's cylinder has a diameter of 8 cm and a height
of 9 cm. Vincent's cylinder has a diameter of 9 cm and a height of 8 cm.
a Find the surface area of Amy's cylinder, rounded to two decimal places.
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b Find the surface area of Vincent's cylinder, rounded to two decimal places.
c Which cylinder has a larger surface area?
21 If a spherical ball with a radius of 4.9 m fits exactly inside a cylinder, find the surface area of
the cylinder rounded to one decimal place.
22 The two identical spherical balls with radii
of 1.8 m fit exactly inside a cylinder.
Find the surface area of the closed cylinder
rounded to one decimal place.
23 Find the surface area of the brickwork for
this silo rounded to two decimal places.
Assume that there is a brick roof and no
floor.
24 A beekeeper has a unique beehive made up of two complete cylinders of beeswax. Imagine
the two cylinders just touch so that there is no overlap. The height of the larger cylinder is
twice the height of the smaller cylinder, and they have the same radius.
a Write down an expression for the total surface area of the beehive. Use h to represent
the height of the smaller cylinder. Leave your answer in terms of π.
b If the total surface area is 336π cm2 , determine the radius of the base of the beehive,
rounded to two decimal places, given that h = 8 cm.
25 At a luxury hotel's lobby, there's an ornate chocolate fountain made from a cylindrical block
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of solid chocolate. This block has been cut in half vertically to allow for a cascade of flowing
chocolate. If the original chocolate cylinder had a height of 2.3 m and a diameter of 150 mm,
how much chocolate surface is exposed after the cut? Round your answer to two decimal
places.
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16.01P Surface area of pyramids and cones - worksheet
Understanding
1 For this net of a cone:
a Which part of the cone corresponds to
the dimension of 18 cm?
b Which part of the cone corresponds to
the dimension of 30 cm?
2 Match the label to the image.
a Right pyramid b Oblique (non-right) pyramid
c Right cone d Oblique (non-right) cone
3 A square-based pyramid has a base area of 20 cm2 and each triangular face has an area of
15 cm2 . How would you find the surface area of the pyramid?
Fluency
4 Find the surface area of the following pyramids, rounded to two decimal places if necessary:
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a Square-based pyramid b Pentagonal-based pyramid with base
area of 440.44 mm2
c Rectangular-based pyramid d Hexagonal-based pyramid with base
area of 314.37 cm2
Example 1
5 The rectangular-based pyramid has
rectangular base with dimensions 6 cm by
8 cm and a perpendicular height of 6 cm.
a Find the value of x, rounded to two
decimal places.
b Find the value of y , rounded to two
decimal places.
c Find the surface area of the pyramid,
rounded to one decimal place.
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Example 2
6 For each of these square-based pyramids:
i Find the length of the slant height, rounded to two decimal places.
ii Find the surface area of the square-based pyramid, rounded to one decimal place.
a b
c d
7 A regular hexagonal-based pyramid has a base area of 36 cm2 and each triangular face has
an area of 14 cm2 . Find the surface area of the pyramid.
8 Find the surface area of these pyramids:
a A square-based pyramid with a base edge of 12 cm and a perpendicular height of 8 cm.
b A rectangular-based pyramid with base dimensions of 4 mm × 12 mm and a perpendicular
height of 8 mm.
c A rectangular-based pyramid with base dimensions of 6 m × 8 m and a perpendicular
height of 10 m.
9 Some very famous right square-based pyramid are the Egyptian Pyramids. The Great
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Pyramid which has a base of 230 m and a slant height of 216 m.
Find the surface area of the Great Pyramid. Do not include the area of the base in your
calculation.
10 For each cone, find the surface area rounded to two decimal places.
a b
c d
Example 3
11 For each cone, find the surface area rounded to two decimal places.
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a b
c d
12 Using the cone measurements:
i Find the slant height of the cone.
ii Calculate the surface area of the cone, rounded to two decimal places.
a Radius = 3 cm, height = 4 cm b Radius = 5 cm, height = 12 cm
c Radius = 12 cm, height = 5 cm d Radius = 15 cm, height = 8 cm
e Radius = 1 m, height = 1 m f Radius = 8 m, height = 5 m
13 This cone has been sliced in half and has a
diameter of 5 cm and a slant height of 11 cm.
Find the surface area of the solid, rounded
to two decimal places.
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Reasoning
14 Show that πr (r + r2 + h2 ) is the expression for the surface area of a cone when radius is r
and height is h.
15 Barney was demonstrating how to find the surface area of the square-based pyramid.
Explain where Barney has gone wrong.
16 Which would have a larger surface area a cone with diameter 10 cm or a square-based
pyramid with base length 10 cm, if they are both have the same perpendicular height?
Explain your reasoning without showing the calculations.
Problem-solving
17 A pyramid has been removed from inside a rectangular prism, as shown in the figure:
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a Find the slant height of the triangle side
with base length 12 cm. Round your
answer to two decimal places.
b Find the slant height of the triangle side
with base length 10 cm. Round your
answer to two decimal places.
c Find the surface area of the composite
solid, rounded to two decimal places.
18 A small square-based pyramid of height
5 cm was removed from the top of a large
square-based pyramid of height 10 cm
leaving the solid shown:
a Find the slant height of the trapezoidal
sides of the new solid. Round your
answer to two decimal places.
b Find the surface area of the composite
solid formed, rounded to one decimal
place.
19 An ice cream cone has a surface area of
20 cm2 .
If the size of the cone is increased by a
scale factor of 3.1, find its new surface area,
rounded to one decimal place.
20 If the height of a cone is scaled by factor of 3 and the radius is scaled by a factor of 2 , find
4 3
an expression for the new surface area in terms of r and h.
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21 An ice cream cone is made by folding
together a sector of pastry, with a small
overlap. The dimensions of the cone are
shown:
a Find the external surface area of the
cone in square centimetres, rounded to
one decimal place.
b If the overlap adds an extra 5% to the
area, determine how much pastry is
required to produce the cone. Round
your answer to the nearest square
centimetre.
22 A grain silo has the shape of a cylinder
attached to a cone, with dimensions as
shown:
a Find the surface area of the silo, to the
nearest square metre, assuming the top
is closed.
b The silo is manufactured out of sheet
metal that has a mass of 2.4 kg/m2 . Find
the total mass of the silo to the nearest
kilogram.
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16.02P Surface area of spheres - worksheet
Understanding
1 Are these statements true or false?
a The surface area of a sphere is always less than the square of its circumference.
b d2
Given the diameter of a sphere, d, we can use the formula SA = 4π .
2
c If you double the radius of a sphere, its surface area will also double.
d The surface area of a sphere is directly proportional to the square of its radius
2 By what factor will the surface area increase if the radius of a sphere is doubled?
3 If the total surface of a sphere is 4πr2 , what is the total surface area of a quarter sphere?
Fluency
4 Find the surface area for each sphere, rounded to two decimal places:
a b
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c d
e f
Example 1
5 Find the radius of the sphere, rounded to two decimal places, where:
a A sphere has a surface area of 370 cm2 .
b A ball has a surface area of 2463.01 mm2 .
6 Calculate the exact surface areas of these spheres with:
a Radius = 2 cm b Radius = 5 cm
c 3 d Radius = 14.9 cm
Radius = m
8
e Diameter = 10 cm f Diameter = 23 mm
7 The planet Earth has a radius of 6370 km. Find the exact surface area of Earth.
8 This dome is a solid hemisphere.
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a Find the area of the curved surface of
the dome, rounded to three decimal
places.
b Find the area of the circular base of the
dome, rounded to three decimal places.
c Find the total surface area of the dome,
rounded to two decimal places.
9 For each hemisphere, find the total surface area rounded to three decimal places.
a b
Example 2
10 The surface area of a sphere is 484π and the diameter is 2(x2 − 14). Solve for x.
11 The circumference of a golf ball is 4.2π cm. Find the surface area of the ball.
Reasoning
12 Explain why doubling the radius of a sphere does not double its surface area.
13 A student was calculating the surface area
of the sphere shown and has these
workings.
3
9
Step 1 SA = 4π × ( )
2
729
Step 2 = π
2
Step 3 ≈ 1145.11 cm2
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Explain what the student's mistake was,
then find the actual surface area of the
sphere.
14 Consider a sphere with a radius of 4 cm and another sphere with a radius of 12 cm. Compare
their surface areas and explain the difference.
Problem-solving
15 The planet Jupiter has a radius of 69 911 km, and planet Mars has a radius of 3390 km. State
approximately how many times bigger the surface area of Jupiter is than Mars.
16 A spherical chocolate truffle has a surface area of 2.25π cm2 .
a Find the radius of the chocolate truffle.
b If 25 chocolate truffles are to be made and sprinkles have a density of 0.2 g/cm2 , how
many grams of sprinkles would be needed? Round the answer to two decimal places.
c The chocolate truffles are packaged in boxes that are 1 truffle wide and 10 truffles long.
Find the dimensions of each box.
17 This shape is constructed by removing a
hemisphere from a cylinder. Report each
calculated measurement to an appropriate
degree of precision.
a Find the surface area of the
hemispherical part.
b Find the surface area of the cylindrical
part, including the circular base.
c Find the total surface area of the shape.
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18 The solid shown is constructed by cutting
out a quarter of a sphere from a cube.
Find its surface area if the side length is
14.2 cm and the radius of the sphere is half
the side length.
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16.03P Surface area of composite solids - worksheet
Understanding
1 What is a composite solid? Give an example.
2 Explain how to calculate the surface area of a composite solid.
3 What basic solids are used to make each of these composite solids?
a b
c d
Fluency
4 The solid shown is made up of a cone and a hemisphere.
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a Calculate the slant height of the cone, giving your answer in exact form.
b Find the surface area of the cone, rounded to two decimal places.
c Find the surface area of the hemisphere, rounded to two decimal places.
d Find the total surface area of the solid, rounded to the nearest square centimetre.
Example 1
5 Find the surface area of these composite solids, rounded to two decimal places:
a b
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c d
e f
Example 2
6 The solid shown is a hemisphere on a
cylinder.
a Find the exact surface area of each of
these faces:
i The circular base.
ii The curved part of the cylinder.
iii The hemisphere.
b Find the total surface area of the solid,
rounded to two decimal places.
7 This solid is made up of a cone and a
hemisphere.
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a Find the surface area of each of these
faces, rounding your answer to two
decimal places:
i The hemisphere.
ii The curved surface of the cone.
iii The torus (doughnut shape).
b Calculate the total surface area of the
solid, rounding your answer to the
nearest square centimetre.
8 The solid shown is constructed by cutting
out a quarter of a sphere from a cube. The
side length of the cube and the diameter of
the sphere are both 6 cm.
a List all of the faces of the solid.
b Find the surface area of the solid.
9 A pyramid has been removed from inside a cube as shown:
a Find the perpendicular height of the
triangular faces, rounding your answer
to two decimal places.
b Find the surface area of the composite
solid, rounded to one decimal place.
10 A small square-based pyramid of height
6 cm was removed from the top of a large
square-based pyramid of height 12 cm to
form the solid shown.
a Find the length of the slant height of the
sides of the new solid, rounded to two
decimal places.
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b Find the surface area of the solid
formed, rounded to one decimal place.
Reasoning
11 The figure shows a cylinder of radius 3 cm,
and its height is double the radius. On the
top and bottom of the cylinder are cones
with radii and height both also equal to 3 cm
.
a Describe the steps involved in
calculating the surface area of this
composite solid.
b Find the surface area of the solid. Round
your answer to two decimal places.
12 An ice creamery sells their ice cream in two different types of waffle 'cones'. One type is a
pointy cone while the other type has a flat base and is made up of two cylinders. Both
'cones' are made with the same thickness of waffle. Which type should a customer buy if
they want the most waffle? Explain your answer.
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Problem-solving
13 An eight-sided die is an octahedron, which
can be thought of as a composite shape
made of two square-based pyramids. Each
face is an equilateral triangle with side
lengths of 1.8 cm.
a Find the perpendicular height of the
equilateral triangle, rounding your
answer to two decimal places.
b Find the surface area of the die. Round
your answer to one decimal place.
c Does the eight-sided die have a greater
surface area than a six-sided die with
side lengths of 1.8 cm?
14 A spire is an architectural feature which originated in the 12th century in Germany and can
be seen throughout Europe in Gothic and Baroque architecture. It has the shape of a cone
or a pyramid.
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a A castle has two spires with square bases. The width of the base is 4 m and the slant
height of each side of the spire is 35 m. Determine how much paint is required to cover
both spires.
b Another castle has two spires with the same slant height as in part (a), but the base of the
spires is a hexagon with side length 2 m. Explain how will this building require more or
less paint than the previous building.
c Assuming they have equal slant heights, determine the side length that the spires with a
hexagonal base need to have in order to require the same amount of paint as the spires
with a square base in part (a).
15 A pedestal for an action figurine is the
shape of the solid made by removing the
top section from a cone. Find the surface
area of the pedestal.
16 The base of a water feature is made of a
rectangular prism of stone from which a
hemisphere has been removed. The entire
surface of the solid, except the underside
which will sit on the ground, must be
polished.
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a Find the surface area of the solid,
excluding the underside. Round your
answer to two decimal places.
b The cost of polishing the stone is
$214/m2 . Determine the total cost of
polishing the water feature base.
17 The water bottle shown can be considered
a composite solid. Calculate the surface
area of the bottle.
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