Nets of 3-Dimensional Figures Matching Nets and 3-D Figures

Face is a flat _____________________ of a solid figure.

Edge is a ____________________ segment where two faces of a
____________________ meet.
Vertex is a ____________________ where ____________________ or more
edges of a solid figure meet or the pointed end of a cone opposite of
its base.
FIGURE FACES Look BASE How many NET
Like faces?

Cube

Rectangular
Prism

Triangular
Prism

Square
Pyramid

Triangular
Pyramid

Cylinder

Cone

Pg.15a pg. 15b

 Using Formulas to Find Surface Area Using Formulas to Find Surface Area
A formula is a mathematical rule using variables. It allows us to So… what exactly IS surface area, anyway?
easily find a value such as area, volume, circumference,
perimeter, etc. Formulas are used often in math and science!

Formulas for Surface Area:

SA Rectangular Prism = 2(l•w) + 2(l•h) + 2(w•h)

Draw a rectangular prism: Draw the net of a rectangular prism:

w
l
How do you think you could calculate the SURFACE AREA of a
RECTANGULAR PRISM?

SA Cube = 6s²

s
Draw a SQARE PYRAMID: Draw the net of a SQARE PYRAMID:

s
s
How do you think you could calculate the SURFACE AREA of a SQARE
PYRAMID?

Pg.16a pg. 16b

 You Try:
Using either method (nets or formulas), find the surface area.
Draw a CUBE: Draw the net of a CUBE:
1)

How do you think you could calculate the SURFACE AREA of a CUBE?

Complete the following statement:

When I need to find the surface area of a 3-dimensional (3-D)

figure, I can do that by…

2) 3)

Pg.17a pg. 17b

4) 5) 8) 9)

10) 11)

6) 7) Find the Surface Area of a

cube with side length 4cm.

Pg.18a pg. 18b

 Surface Area in the Real World 4) Sydney is painting a rectangular toy box for her little brother.
She will paint all 4 sides and the top (she will NOT paint the
Solve each of the problems by drawing a net and finding the surface bottom). If the toy box is 20 inches tall, 12 inches wide, and
area.
25 inches long, how many square inches will she need to
1) A pizza box is 15 inches wide, 14 inches long, and 2 inches tall. paint?
How many square inches of cardboard were used to create the
box?

2) What is the surface area of a Rubik’s Cube that is 6 cm tall?

5) DeAndre is making a tent for his hamster. It is 20 cm long,
and the triangular bases are 15 cm high and 10 cm wide
(see picture below). How much material will he need to
make the tent?

20 cm

3) Angelo is making a replica of an Egyptian pyramid. He is making a

square pyramid with a base that is 3 feet long and 3 feet wide.
The triangular sides of the pyramid each have a height of 14 feet.
How much material will Angelo need to cover the pyramid?

Pg.19a pg. 19b

 Volume of Rectangular Prisms Volume is the _________________ of __________________ units
needed to fill the space in a three dimensional (3D) figure.
Volume is the amount of space inside a 3D object, measured in
Volume is always measured in cubic units.
cubic units.
We calculate volume you must find the area of the ____________
Ever wonder WHY volume is
then multiply it by the _____________________.
measured in cubic units??
This can be written as __________ • __________.

OR __________ • __________ • __________ for a rectangular prism.

Since volume measures the amount of
space INSIDE a figure, it’s like you’re Example:
packing the figure with little tiny cubes!!
Hence, Find the volume of the rectangular prism below.

Here’s a visual of “cubic units”. Cool,

a rectangular huh? ☺ V=B•h
prism being
packed with unit
V=l•w•h
cubes… V=4•4•6
V = 96 cm3

You Try:
72 Cubic Units
Find the volume.
1) 2)
Here’s a visual of
a cube being
packed with unit
cubes…

Pg.20a pg. 20b

 3) 4) Volume of Rectangular Prisms with Fractional Edges

5) Find the volume of a 6) Find the volume of a

rectangular prism with B = rectangular prism with l =
78ft2 and h = 23 ft. 4.2cm, w = 3.8cm, and h =
6cm.

7) Find the volume of a 8) Find the missing dimension of

rectangular prism with l = 8 ¼ the rectangular prism.
in., w = 9in and h = 15in. L = 14 cm
W=?
H = 3 cm
V = 294 cm
You Try:
Find the volume of a rectangular prism with a length of 3cm, a
width of 2 ½ cm, and a height of 4 cm.

Pg.21a pg. 21b

 Volume Error Analysis More Volume Practice
Sally is a silly little girl that makes silly mistakes! CHOOSE ANY 4 Determine the Volume of each rectangular prism or cube
PROBLEMS BELOW. Analyze her work in Column #1, and circle her below. Include units and show your work!
mistake. In Column #2, explain what she did wrong. In Column
#3, show how Silly Sally should work out the problem. Show ALL 1. A cube that is 12 yards wide
work!
Show Silly Sally how it’s
Silly Sally’s Work What did Silly
done!
(Circle her mistake): Sally do wrong?
(Show ALL steps!)

V = lwh
V=4•4•4 2. The box with dimensions of 6 ft • 4 ft • 1 ½ ft
4m V= 12 m³

2mm V=lwh
V=8•½•2
1 3. Determine the Volume of a rectangular truck bed that is 12
8mm 2
mm V=4•2
V = 8mm2 feet long, 5 ¼ feet wide, and 3 feet deep.

V = lwh
2 2 2
V= ∙ ∙
3 3 3
6 2
V = = in3
Cube = 2/3 in. tall 9 3
4. How much water can be poured into a cubic tank that is 2 ½
feet long?
V=lwh
8 ¼ yd V=8¼ •2½•3
1
V = 16 • 3
8
1
2 ½ yd V = 48 yd3
3 yd 8

5. What is the volume of a gift box that is 3 ½ inches wide, 2

V=lwh
8 yd
1
inches tall, and 6 inches long?
4 V=4½•1½•2
8 3
V= • •2
1 2 2
1 yd 24
2 yd
2 V= •2
4
V = 12 yd3

Pg.22a pg. 22b