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1 Find the total surface area of a cuboid with length 8 cm, width 6 cm and height 3 cm.
2 A box, in the shape of a cuboid, has volume
357 cm3.
It has a length of 8.5 cm and a width of 6 cm.
Calculate the height of the box.
3 Work out the area of a rectangle that is 9.5 m long and 6.8 m wide.
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5 cm
4 cm
7 cm
Calculate the total surface area of this cuboid.
1 mile = 1.609344 kilometres
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Change 6 miles into metres.
Give your answer correct to the nearest metre.
The diagram shows a sector of a circle with radius 4.8 cm and sector angle 45°.
Calculate the area of the sector.
7 Find the radius of a hemisphere of volume 80 cm3.
The diagram shows a right-angled triangular prism.
Work out the volume of the prism.
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The diagram shows a circle inside a square.
The circle touches the four sides of the square.
The area of the square is 81 cm2.
Calculate the shaded area.
The diagram shows a solid metal shape made from a cone and a hemisphere, both with radius 6.2 cm.
The total surface area of the solid shape is 600 cm2.
Calculate the slant height, l, of the cone.
[The surface area, A, of a sphere with radius r is .]
[The curved surface area, A, of a cone with radius r and slant height l is .]
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4m
0.45 m
The diagram shows a horizontal container for water with a uniform cross-section.
The cross-section is a semicircle.
The radius of the semicircle is 0.45 m and the length of the container is 4 m.
(a) Calculate the volume of the container.
(b)
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0.3 m
The greatest depth of the water in the container is 0.3 m.
The diagram shows the cross-section.
Calculate the number of litres of water in the container.
Give your answer correct to the nearest integer.
11 The volume of a solid cone is 310 cm3.
The height of the cone is twice the radius of its base.
Calculate the slant height of the cone.
[The volume, V, of a cone with radius r and height h is .]
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12 A solid metal cube of side 20 cm is melted down and made into 40 solid spheres, each of radius r cm.
Find the value of r.
[The volume, V, of a sphere with radius r is .]
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A solid cylinder has radius x cm and height cm.
The surface area of a sphere with radius R cm is equal to the total surface area of the cylinder.
Find an expression for R in terms of x.
[The surface area, A, of a sphere with radius r is .]
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A rectangular sheet of paper ABCD is made into an open cylinder with the edge AB meeting the edge DC.
AD = 28 cm and AB = 20 cm.
(a) Show that the radius of the cylinder is 4.46 cm, correct to 3 significant figures.
(b) Calculate the volume of the cylinder.
(c) N is a point on the base of the cylinder, such that BN is a diameter.
Calculate the angle between AN and the base of the cylinder.
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O
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x°
A B
2.4 cm AB
The volume of a paper cone of radius 2.4 cm is 95.4 cm3.
The paper is cut along the slant height from O to AB.
The cone is opened to form a sector OAB of a circle with centre O.
Calculate the sector angle x°.
[The volume, V, of a cone with radius r and height h is .]
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16 O
60°
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24 cm SCALE
P Q
The diagram shows a sector OPQ of a circle with centre O and radius 24 cm.
The sector angle is 60°.
A cone is made from this sector by joining OP to OQ.
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P
Q
Calculate the volume of the cone.
[The volume, V, of a cone with radius r and height h is .]
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B C
The diagram shows a shape made from an equilateral triangle ABC and a sector of a circle.
Points B and C lie on the circle, centre A.
The side length of the equilateral triangle is 12.4 cm.
Work out the perimeter of the shape.
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41°
The diagram shows two sectors of a circle.
The major sector is shaded.
The area of the major sector is 74.5 cm2.
Calculate the radius of the circle.
19 A cylinder with radius 6 cm and height h cm has the same volume as a sphere with radius 4.5 cm.
Find the value of h.
[The volume, V, of a sphere with radius r is .]
