Volume of Rectangular Prisms

1. Volume is the amount of 3-dimensional space a solid takes up. It is measured in cubic units.

A rectangular prism is filled with unit cubes. Count the cubes to find the volume.

• Layer 1 (bottom): $4$ columns $\times$ $3$ rows $=$ $\underline{\quad}$ cubes
• Layer 2 (top): same as Layer 1 $=$ $\underline{\quad}$ cubes

Total volume $= \underline{\quad} + \underline{\quad} = \underline{\quad}$ cubic units

2. Use the formula $V = l \times w \times h$ to find the volume.

a) A box: length $= 5$ cm, width $= 4$ cm, height $= 3$ cm

$V = \underline{\quad} \times \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ cm}^3$

b) A cube: all sides $= 6$ inches

$V = \underline{\quad} \times \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ in}^3$

c) A fish tank: length $= 12$ inches, width $= 6$ inches, height $= 8$ inches

$V = \underline{\quad} \times \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ in}^3$

3. A rectangular prism has a volume of $60$ cubic centimeters.

Its length is $5$ cm and its width is $4$ cm. What is its height?

$V = l \times w \times h$ $60 = 5 \times 4 \times h$ $60 = 20 \times h$ $h = \underline{\quad} \text{ cm}$

4. A shipping box is $10$ inches long, $8$ inches wide, and $6$ inches tall.

a) What is the volume of the box?

$V = \underline{\quad} \times \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ in}^3$

b) Each book inside is $2$ inches $\times$ $2$ inches $\times$ $1$ inch.

Volume of one book: $V = \underline{\quad} \times \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ in}^3$

c) How many books can fit in the box (assume perfect packing with no gaps)?

$\text{Number of books} = \frac{\underline{\quad}}{\underline{\quad}} = \underline{\quad}$

5. A composite solid is made of two rectangular prisms joined together.

• Prism A: $6$ m $\times$ $4$ m $\times$ $3$ m
• Prism B: $2$ m $\times$ $4$ m $\times$ $5$ m

$V_A = \underline{\quad} \times \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ m}^3$

$V_B = \underline{\quad} \times \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ m}^3$

$V_{\text{total}} = \underline{\quad} + \underline{\quad} = \underline{\quad} \text{ m}^3$

6. Two boxes have the same volume of $120 \text{ cm}^3$.

Box 1: length $= 10$ cm, width $= 4$ cm, height $= \underline{\quad}$ cm

Box 2: length $= 6$ cm, width $= 5$ cm, height $= \underline{\quad}$ cm

Find the missing heights:

Box 1: $10 \times 4 \times h = 120 \Rightarrow h = \underline{\quad}$ cm

Box 2: $6 \times 5 \times h = 120 \Rightarrow h = \underline{\quad}$ cm

If both boxes were used as containers for water, would they hold the same amount? $\underline{\qquad\qquad}$