What is the ratio of the length of the body diagonal of a cube to the face diagonal of the cube?

Name: What is the ratio of the length of the body diagonal of a cube to the face diagonal of the cube?
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Question

Quizplus · Accepted Answer

The body diagonal of a cube can be found using the formula $\sqrt{3}a$ where $a$ is the side length, and the face diagonal using $\sqrt{2}a$. The ratio of the body diagonal to the face diagonal is $\frac{\sqrt{3}a}{\sqrt{2}a} = \sqrt{\frac{3}{2}}$, which simplifies to approximately 1.22.

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