220. Volume of Right Prisms

Learning Intentions

• Apply the prism volume formula Use base area and height.
• Calculate volumes of rectangular and triangular prisms.
• Interpret volume using cubic units.

Pre-requisite Summary

• A right prism has two congruent, parallel bases.
• The height of a prism is the perpendicular distance between the two bases.
• The volume of a prism is calculated using .
• The base area must be found before multiplying by the prism height.
• A rectangular prism has volume .
• A triangular prism has base area .
• Volume is measured in cubic units such as , and .
• Cubic units describe how many unit cubes fit inside a solid.

Worked Examples

Worked Example 1

A right prism has base area and height .

Find the volume.

Worked Example 2

A right prism has volume and base area .

Find the height of the prism.

Worked Example 3

A rectangular prism has length , width and height .

Find the volume.

Worked Example 4

A triangular prism has a triangular base with base length and perpendicular height . The length of the prism is .

Find the volume.

Worked Example 5

A rectangular prism has dimensions:

Find the volume and state the answer using correct cubic units.

Worked Example 6

A triangular prism has a triangular base with base length and perpendicular height . The prism height is .

Find the volume and interpret what the cubic unit means.

Problems

Problem 1

A right prism has base area and height .

Find the volume.

Problem 2

A right prism has volume and base area .

Find the height of the prism.

Problem 3

A rectangular prism has length , width and height .

Find the volume.

Problem 4

A triangular prism has a triangular base with base length and perpendicular height . The length of the prism is .

Find the volume.

Problem 5

A rectangular prism has dimensions:

Find the volume and state the answer using correct cubic units.

Problem 6

A triangular prism has a triangular base with base length and perpendicular height . The prism height is .

Find the volume and interpret what the cubic unit means.

Exercises

Understanding and Fluency

Exercise 1

Find the volume of a right prism with base area and height .

Exercise 2

Find the volume of a right prism with base area and height .

Exercise 3

A right prism has volume and base area .

Find the height.

Exercise 4

A right prism has volume and height .

Find the base area.

Exercise 5

Find the volume of a rectangular prism with dimensions:

Exercise 6

Find the volume of a rectangular prism with length , width and height .

Exercise 7

A triangular prism has triangular base length , triangular perpendicular height and prism length .

a) Find the area of the triangular base.

b) Find the volume of the prism.

Exercise 8

A triangular prism has triangular base length , triangular perpendicular height and prism length .

a) Find the area of the triangular base.

b) Find the volume of the prism.

Exercise 9

Choose the correct unit for the volume of each object.

a) A small cardboard box measured in centimetres

b) A swimming pool measured in metres

c) A tiny plastic component measured in millimetres

Exercise 10

Complete each statement.

a) If length is measured in , then volume is measured in .

b) If length is measured in , then volume is measured in .

c) If length is measured in , then volume is measured in .

Reasoning

Exercise 11

Explain why the formula for the volume of any right prism can be written as:

Exercise 12

A student calculates the volume of a triangular prism using:

Explain what part of the calculation is missing.

Exercise 13

A rectangular prism and a triangular prism both have the same height of .

The rectangular prism has base area and the triangular prism has base area .

Explain why their volumes are equal.

Exercise 14

A student gives the volume of a rectangular prism as .

Explain why the unit is incorrect.

Problem-solving

Exercise 15

A storage box is a rectangular prism with length , width and height .

a) Find the volume.

b) State the answer using cubic units.

c) Explain what the volume represents.

Exercise 16

A tent is shaped like a triangular prism. The triangular end has base length and perpendicular height . The tent is long.

a) Find the area of the triangular end.

b) Find the volume of the tent.

c) Explain why the answer is measured in .

Exercise 17

A right prism has volume and height .

a) Find the area of the base.

b) Suggest possible dimensions for a rectangular base with this area.

c) Explain why more than one rectangular base is possible.

Exercise 18

Two rectangular prisms are shown.

Prism A has dimensions:

Prism B has dimensions:

a) Find the volume of Prism A.

b) Find the volume of Prism B.

c) Compare the volumes.

Potential Misunderstandings

• Thinking the base of a prism must always be the bottom face.
• Confusing the height of the prism with the height of a triangular base.
• Forgetting to find the triangular base area before calculating the volume of a triangular prism.
• Using instead of for a triangular base.
• Writing volume answers using square units instead of cubic units.
• Multiplying only two dimensions when finding the volume of a rectangular prism.
• Using a slanted side length instead of the perpendicular height.
• Assuming prisms with different shapes cannot have the same volume.
• Forgetting that applies to all right prisms.

Next: 221. Volume of Cylinders