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A rectangular prism has a volume of $693 \, \text{cubic centimeters}$ . The prism has a width of $9 \, \text{centimeters}$ and a height of $7 \, \text{centimeters}$ . Which equation can you use to find the length of the prism, $\ell$ ? $\newline$ Choices: $\newline$ (A) $9 \times 7 = 693 \times \ell$ $\newline$ (B) $\ell \times 9 \times 7 = 693$ $\newline$ What is the length of the prism? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ ____ inches

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. A rectangular prism has a volume of

693 \, \text{cubic centimeters}

. The prism has a width of

9 \, \text{centimeters}

and a height of

7 \, \text{centimeters}

. Which equation can you use to find the length of the prism,

\ell

?

\newline

Choices:

\newline

(A)

9 \times 7 = 693 \times \ell

\newline

(B)

\ell \times 9 \times 7 = 693

\newline

What is the length of the prism?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ inches

Identify formula: Identify the correct formula to use for calculating the length of the prism. Given the volume formula for a rectangular prism is $\text{Volume} = \text{length} \times \text{width} \times \text{height}$ , rearrange to find length, $\ell = \frac{\text{Volume}}{(\text{width} \times \text{height})}$ .
Plug in values: Plug in the given values into the rearranged formula. $\ell = \frac{693}{(9 \times 7)}$ .
Calculate value: Calculate the value of $\ell$ . $\ell = \frac{693}{63}$ .
Simplify division: Simplify the division to find the length. $\ell = 11$ .

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