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Students in Mrs. Johnson's class can win prizes like colorful pencils and fun-shaped erasers for performing acts of kindness. Mrs. Johnson displays the prizes in a glass case shaped like a rectangular prism. It has a length of $18$ inches, a height of $3$ inches, and a volume of $270$ cubic inches. $\newline$ Which equation can you use to find the width of the prize case, $w$ ? $\newline$ Choices: $\newline$ (A) $270 \times 18 \times 3 = w$ $\newline$ (B) $18 \times w \times 3 = 270$ $\newline$ What is the width of the prize case? $\newline$ 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

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Q. Students in Mrs. Johnson's class can win prizes like colorful pencils and fun-shaped erasers for performing acts of kindness. Mrs. Johnson displays the prizes in a glass case shaped like a rectangular prism. It has a length of

18

inches, a height of

3

inches, and a volume of

270

cubic inches.

\newline

Which equation can you use to find the width of the prize case,

w

?

\newline

Choices:

\newline

(A)

270 \times 18 \times 3 = w

\newline

(B)

18 \times w \times 3 = 270

\newline

What is the width of the prize case?

\newline

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

\newline

____ inches

Identify correct formula: First, let's identify the correct formula to find the width of the prize case. We know the formula for the volume of a rectangular prism is $V = \text{length} \times \text{width} \times \text{height}$ . Here, $V = 270$ cubic inches, length = $18$ inches, and height = $3$ inches. We need to solve for width ( $w$ ). The correct equation from the choices given is: $\newline$ (B) $18 \times w \times 3 = 270$
Use correct formula: Now, let's solve the equation for $w$ . Start by dividing both sides of the equation by the product of the length and the height to isolate $w$ : $w = \frac{270}{(18 \times 3)}$ $w = \frac{270}{54}$ $w = 5$

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