126. Volume and Capacity of Rectangular Prisms

126. Volume and Capacity of Prisms

Learning Intentions

• To understand that volume is the space occupied by a three-dimensional object
• To understand that capacity is the volume of fluid or gas that a container can hold
• convert between units for volume and capacity
• Solve the volume of rectangular prisms, including cubes

Pre-requisite Summary

• Know that three-dimensional objects have length, width and height. See 092. Volume of Rectangular Prisms
• Understand that area measures the amount of surface inside a two-dimensional shape. See 125e. Nets and Surface Area of Prisms
• Know that volume measures space in three dimensions.
• Understand that volume is measured in cubic units such as and
• Understand that capacity is commonly measured in mL, L and kL
• Know basic metric conversions such as . 094r. Capacity and Volume Conversions
• Know that a cube is a special rectangular prism with all edges equal. 092. Volume of Rectangular Prisms
• Be able to multiply whole numbers and decimals accurately. 005. Multiplication Laws and Algorithms, and 044. Multiplying Decimals

Worked Examples

Worked Example 1

State the meaning of each term and Identify a suitable unit:

a) volume of a box

b) capacity of a water bottle

c) capacity of a swimming pool

Worked Example 2

Convert between units for volume and capacity:

a) to L

b) to mL

c) to L

Worked Example 3

Convert between units for volume and capacity:

a) to L

b) to

c) to L

Worked Example 4

Find the volume of each rectangular prism:

a) length , width , height

b) length , width , height

Worked Example 5

Find the volume of each cube:

a) side length

b) side length

Worked Example 6

A fish tank is a rectangular prism with length , width and height .

a) Find its volume in

b) Convert this volume to litres

Problems

Problem 1

State the meaning of each term and identify a suitable unit:

a) volume of a cupboard

b) capacity of a milk carton

c) capacity of a dam

Problem 2

Convert between units for volume and capacity:

a) to L

b) to mL

c) to L

Problem 3

Convert between units for volume and capacity:

a) to L

b) to

c) to L

Problem 4

Find the volume of each rectangular prism:

a) length , width , height

b) length , width , height

Problem 5

Find the volume of each cube:

a) side length

b) side length

Problem 6

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

a) Find its volume in

b) Convert this volume to litres

Exercises

Understanding and Fluency

Exercise 1.

Complete each statement:

a) Volume is the amount of ______ occupied by a 3D object

b) Capacity is the amount of fluid or gas a ______ can hold

c) Volume is measured in ______ units

d) Capacity is often measured in ______ and ______

Exercise 2.

State whether each measure is volume or capacity:

a) the amount of space inside a cardboard box

b) the amount of juice a bottle can hold

c) the amount of space occupied by a brick

d) the amount of water a tank can hold

Exercise 3.

Convert between units for capacity:

a) to L

b) to mL

c) to L

d) to L

Exercise 4.

Convert between units for volume and capacity:

a) to L

b) to

c) to L

d) to L

Exercise 5.

Find the volume of each rectangular prism:

a)

b)

c)

Exercise 6.

Find the volume of each cube:

a) side length

b) side length

c) side length

Exercise 7.

Find the volume, then convert where needed:

a) a prism , answer in and L

b) a cube with side , answer in and L

c) a prism , answer in and L

Exercise 8.

Solve each:

a) A rectangular prism has length , width and height . Find its volume

b) A cube has volume . Find its side length

c) A container has capacity . Write this in mL and

Reasoning

Exercise 9.

Explain why volume is measured in cubic units instead of square units.

Exercise 10.

A student says that the volume of a rectangular prism is found by adding length, width and height. Explain the mistake.

Exercise 11.

Noah says that . Is he correct? Explain.

Exercise 12.

Explain why capacity and volume are closely related but not exactly the same idea.

Exercise 13.

A student says that a cube with side length has volume . Describe the error.

Problem-solving

Exercise 14.

A lunchbox measures by by . Find its volume.

Exercise 15.

A carton has capacity . Write this capacity in mL and .

Exercise 16.

A fish tank measures by by . Find its volume in and litres.

Exercise 17.

A cube-shaped container has side length . Find its volume.

Exercise 18.

A swimming pool contains of water. Convert this to litres.

Exercise 19.

A storage box has volume . Its length is and its width is . Find its height.

Potential Misunderstandings

• Students may confuse volume with area or perimeter
• Students may think capacity and volume mean exactly the same thing in every context
• Students may Use square units instead of cubic units for volume
• Students may forget that
• Students may forget that
• Students may forget that
• Students may add dimensions instead of multiplying them when finding volume
• Students may think the volume of a cube is found by doubling or squaring its side length instead of cubing it
• Students may confuse the units when converting between volume and capacity
• Students may not Check whether their final answer is reasonable for the size of the object

Next: 127. Volume of Prisms and Cylinders