Volume of Prisms and Cubes Bell
Ringers
Calculate the area of the following shapes.
1.
3.
2.
4.
Created by: Melissa Forsyth
5.
7.G.6 Volume of Prisms and
Cubes
Created By: Melissa Forsyth
What is volume?
Volume is the measurement of how much space
a three dimensional object takes up. It is the
number of cubic units that will exactly fill a given
shape.
Created by: Melissa Forsyth
What is a cube?
A cube is a region of space formed by six
identical square faces joined along their edges.
Three edges join at each corner to form a vertex.
Created by: Melissa Forsyth
Parts of a cube
Face: Also called facets or sides. A cube has six faces
which are all squares, so each face has four equal sides
and all four interior angles are right angles.
Edge: A line segment formed where two edges meet. A
cube has 12 edges. Because all faces are squares and
congruent to each other, all 12 edges are the same
length.
Vertex: A point formed where three edges meet. A cube
has 8 vertices.
Created by: Melissa Forsyth
How do we calculate the volume of a
cube
Recall that a cube has all edges the same length.
The volume of a cube is found by multiplying the
length of any edge three times.
• So if the length of an edge is 4, the volume is 4 x
4 x 4 = 64
To find the volume of the a cube we use the
formula:
V = s3
V = volume
s = the length of any edge of the cube.
Created by: Melissa Forsyth
Calculate the volume of the following
cube
V = s3
V = 23
V=2x2x2
V = 8 m3 (cubic meters)
Created by: Melissa Forsyth
If the side of a cube is 3.5 inches, find its
volume.
Created by: Melissa Forsyth
Find the side length of the following
cube
This cube has a volume of 27 m3. What are the
lengths of its sides?
V = s3
27 = s3
3
27
What number times itself three times is
27?
3 x 3 x 3 = 27
s = 3m
Created by: Melissa Forsyth
The volume of a cube is 125 ft3. What is the
length of its sides?
Created by: Melissa Forsyth
How do we calculate the volume of
rectangular prism?
To calculate the volume of a rectangular prism you will use the
formula:
V=LxWxH
V = volume
L = Length
W = width
H = height
It doesn't matter what order you multiply these together. You will get
the same answer regardless of the order.
Also, the terms length, width, and height are just words to help you
remember the formula. It doesn't matter which side is which.
Created by: Melissa Forsyth
Calculate the volume of the following
rectangular prism
V=LxWxH
V=4x2x3
V = 24 cm3
Created by: Melissa Forsyth
Calculate the volume of the following
rectangular prism
V=LxWxH
V=9x5x9
V = 405 cm3
Created by: Melissa Forsyth
Calculate the length of the following
rectangular prism
V=LxWXH
168 = L x 3 x 7
V = 168 cm3
168 = L x 21
168
21
=
21𝐿
21
8=L
Length = 8 cm
Created by: Melissa Forsyth
Calculate the height of the following
rectangular prism
V=LxWXH
288 = 9 x 4 x H
V = 288 cm3
288 = 36 x H
288
36
=
36𝐿
36
8=L
Length = 8 cm
Created by: Melissa Forsyth
How do you calculate the area of a
prism
To calculate the area of any given prism you will
use the following formula:
V = Area of base x length
Calculate the area of the following
prism
First calculate the area of the base
𝑏𝑎𝑠𝑒 𝑥 ℎ𝑒𝑖𝑔ℎ𝑡
2
3𝑥8
2
= 12
Now multiply the area of
the base by the height of
the prism:
12 x 7 = 84 m3
Calculate the volume of the following
prism
How do you calculate the volume of a
pyramid?
To calculate the volume of a pyramid you will
use the following formula:
V=
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝐵𝑎𝑠𝑒 𝑥 𝐻𝑒𝑖𝑔ℎ𝑡
3
Calculate the area of this square
pyramid
First you need to find the area of the
base using the formula A = L x W
3 x 5 = 15
Next you need to multiply the area of
the base by the height
15 x 4 = 60 in3
Calculate the area of this triangular
pyramid
How do we calculate the volume of
compound 3D shapes
To the volume of 3D shapes we just need to simplify. We need to
create shapes that we can easily calculate the volume of.
4 cm
Let’s cut it here.
I see that this irregular 3D shape can be cut into two rectangular prisms.
Created by: Melissa Forsyth
How do we calculate the volume of
compound 3D shapes
1 cm
2 cm
5 cm
5 cm
5 cm
5 cm
Now we simply find the dimensions of the two rectangular prisms.
Created by: Melissa Forsyth
How do we calculate the volume of
compound 3D shapes
1 cm
2 cm
5 cm
5 cm
5 cm
5 cm
Now we simply find the volume of both prisms.
Prism A: 5 x 5 x 2= 50 cm3
Prism B: 5 x 5 x 1 = 25 cm3
Now simply add both volumes: 50 + 25 = 75 cm3
Created by: Melissa Forsyth
Calculate the volume
Prism A: 8 x 36 x 40 = 11520
Prism B: 36 x 30 x 32 = 34560
11520 + 34560 = 46080 in3
Created by: Melissa Forsyth
Calculate the volume
Created by: Melissa Forsyth
Calculate the volume
Created by: Melissa Forsyth