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CEMC Gauss (Grade 7), 2016

Geometry Difficulty 1.4 Junior Find the answer Canada

A larger cube has volume 64 cm $^3$ . A smaller cube has edges that are half the length of the edges of the larger cube. What is the volume of the smaller cube?

Pick one

Solution

Since a cube is a rectangular prism, its volume is equal to the area of its base, $l\times w$ , multiplied by its height, $h$ .

A cube has edges of equal length and so $l=w=h$ .

Thus, the volume of a cube is the product of three equal numbers.

The volume of the larger cube is 64 cm $^3$ and $64=4\times4\times4$ , so the length of each edge of the larger cube is 4 cm.

The smaller cube has edges that are half the length of the edges of the larger cube, or 2 cm.

The volume of the smaller cube is $2\times2\times2=8$ cm $^3$ .

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