2002 CEMC Gauss (Grade 8) Problems/Problem 7

Problem

The volume of a rectangular box is $144 \text { cm}^{3}$ . If its length is $12 \text { cm}$ and its width is $6 \text { cm}$ , what is its height?

$\textbf{(A)}\ 126 \text { cm} \qquad\textbf{(B)}\ 72 \text { cm} \qquad\textbf{(C)}\ 4 \text { cm} \qquad\textbf{(D)}\ 8 \text { cm} \qquad\textbf{(E)}\ 2 \text{ cm}$

Solution 1

Let $h$ be the height of the rectangular box.

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Using the formula for the volume of a rectangular prism, we have:

$12 \text { cm} \times 6 \text { cm} \times h = 144 \text{ cm}^{3}$

$72 \text { cm}^{2} \times h = 144 \text { cm}^{3}$

$h = \frac{144 \text { cm}^{3}}{72 \text { cm}^{2}} = \boxed {\textbf {(E) } 2 \text { cm}}$

~anabel.disher

2002 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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2002 CEMC Gauss (Grade 8) Problems/Problem 7

Problem

Solution 1