2006 CEMC Pascal Problems/Problem 5

Problem

In the diagram, the rectangular solid and the cube have equal volumes.

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The length of each edge of the cube is

$\text{ (A) }\ 2 \qquad\text{ (B) }\ 4 \qquad\text{ (C) }\ 8 \qquad\text{ (D) }\ 15 \qquad\text{ (E) }\ 13$

We can use the volume of a rectangular prism to find the side length of the cube.

Let $V$ be the volume of the rectangular solid that we know the side length of. We can then set up an equation involving $V$ :

$V = 2 \times 4 \times 8 = 8 \times 8 = 64$

Let $l$ be the length of each edge of the cube.

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Since a cube is a special rectangular prism, where all of the lengths are equal to each other, its volume must be $l^3$ . This means:

$l^3 = V = 64$

$l = \sqrt[3]{64} = 4$

~anabel.disher