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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) $\ell \times 9 \times 7 = 693$ $\newline$ (B) $9 \times 7 = 693 \times \ell$ $\newline$ 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)

\ell \times 9 \times 7 = 693

\newline

(B)

9 \times 7 = 693 \times \ell

\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 find the length of the prism. Given the volume, width, and height, the formula for volume $V$ of a rectangular prism is $V = \text{length} \times \text{width} \times \text{height}$ . Therefore, the correct equation to find the length $\ell$ is $\ell \times \text{width} \times \text{height} = \text{volume}$ .
Plug in values: Plug in the given values into the equation. Using the values width = $9 \, \text{cm}$ , height = $7 \, \text{cm}$ , and volume = $693 \, \text{cm}^3$ , the equation becomes $\ell \times 9 \times 7 = 693$ .
Solve for $\ell$ : Solve for $\ell$ . Simplify the left side of the equation: $9 \times 7 = 63$ . So, $\ell \times 63 = 693$ . Now, divide both sides by $63$ to isolate $\ell$ : $\ell = \frac{693}{63}$ .
Calculate $\ell$ : Calculate $\ell$ . Perform the division: $693 / 63 = 11$ . Therefore, the length of the prism is $11$ cm.

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