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Problem 154

Geometry Difficulty 1.4 Multiple choice CEMC Pascal · Canada · 2023

A rectangular prism has a volume of $12\text{ cm}^3$ . A new prism is formed by
doubling the length, doubling the width, and tripling the height of the
original prism. The volume of this new prism is

Pick one

Official solution

Suppose that the original prism has length $\ell$ cm, width $w$ cm, and height $h$ cm.

Since the volume of this prism is $\$12\text{}$
cm}^3 $, then$ $\ell$ wh =
12$.

The new prism has length $2\ell$ cm,
width $2w$ cm, and height $3h$ cm.

The volume of this prism, in $\text{cm}^3$ , is $\$(2l)\times$ (2w) $\times$ (3h) = 2 $\times 2 \times 3 \times$ lwh = 12 $\times$ 12 = 144$.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.