Math 2
Lesson 6-7: Volume of Prisms
Name ________________________________
Date ____________________________
Learning Goals:
 I can identify the base for prisms.
 I can set up and solve equations involving the formula for prisms: 𝑉 = 𝐵 ∙ ℎ .
Rectangular prism
Rectangular prism
Triangular prism
Notes:
Practice:
1. Find the volume of the prism pictured to the right.
2. Find the volume of each prism.
cylinder
3. Find the volume of the prism if the area of the base (triangle) is 15 cm2 and the height is
18.6 cm.
4. Find the volume of the cylinder.
5. The volume of a rectangular box is 2400 units3. The measurements of the base are 60
units by 20 units. What is the height of the box?
6. Your cousin works for a company that makes aluminum cans. A large soup can have a
radius of 8 centimeters and a height of 20 centimeters. What is the volume of the can?
7. A local movie theater sells popcorn in boxes. A box measures 2 inches by 5 inches by 10
inches. The theater is considering selling a bigger box that is the same height but the base
dimensions are doubled. Should the theater charge twice as much for this size box of
popcorn? Please support your answer with mathematics.
8. Find the height of a cylinder that has a volume of 325 in3 and a radius of 5 inches.
9. You are helping to build a sandbox for your younger cousin. The base of the sandbox is a
square with a side length of 5 feet. The edge of the sandbox is 8 inches tall. You buy 20
cubic feet of sand. How much sand remains if you fill the sandbox to the top? Show all of
your work.
Homework:
1. The amount of space inside the speaker cabinet is important because it can affect the
sound coming out of a speaker. Consider the speaker cabinet below. This cabinet is in the
shape of a rectangular prism.
a. Imagine a layer of cubes on the bottom of the speaker cabinet shown. Each cube is
one inch long, one inch wide, and one inch tall. How many cubes are in the layer?
Use a complete sentence in your answer.
b. Suppose you add another layer of cubes onto the existing layer. How many cubes are
there in the two layers? Use a complete sentence in your answer.
c. Suppose you add another layer of cubes onto the first two layers. How many cubes
are there in the three layers? Use a complete sentence in your answer.
d. How many cubes will it take to fill the speaker cabinet? Use a complete sentence in
your answer.
2. An 8.5-inch by 11-inch sheet of paper can be rolled along the longer side to make the
cylinder shown on the left. The sheet of paper can be rolled along the shorter side to
make the cylinder shown on the right. Which container can hold more popcorn? Use
complete sentences to justify your reasoning.
3. A football field that is 120 yards long and 65 yards wide is being converted into a cement
parking lot. The cement lot will be 4 inches thick. Find the number of cubic yards of
cement needed to construct the parking lot.
4. A can of juice has a height of 11 centimeters and a diameter of 5 centimeters. A fridge
pack of juice consists of 12 cans stacked in a box in two rows of six. The cans touch the
box on all sides. Find the volume of the empty space in the box.
5. After looking at a cube with a side measure of 1 inch, Lily states that the second cube
with a side measure of 2 inches has a volume that is twice as big as the first cube’s
volume. Is Lily correct? Justify your answer. If she is incorrect, do the mathematics to
find out how much bigger the second cube’s volume is when compared to the first cube’s
volume.
6. Each edge of a larger cube is 3 times longer than each edge of a smaller cube. Complete
the statement below and use a complete sentence to justify your conclusion. The volume
of a larger cube is ______ times larger than the volume of the smaller cube.
7. Three tennis balls are stacked vertically to the top of a cylindrical container. The radius of
each ball and the container is 4 centimeters. (To find the volume of the tennis ball you
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need the formula for the volume of a sphere: V   r 3 )
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a. Find the volume of each tennis ball.
b. Find the volume of the cylindrical container.
c. Is the volume of one tennis ball less than, greater than, or equal to the amount of
empty space in the container? Justify your answer.
8. The rain gutter on my house is 480 in long and the ends are trapezoids with an area of 30
in2. Find the amount of water it could hold if the gutter was clogged.
9. A right triangular prism has a height of 18 in. Its bases are isosceles triangles with side
lengths of 13 in, 13 in, and 10 in. Find the volume of the prism.