Question

A diagonal of a cube measures StartRoot 294 EndRoot cm. The diagonal of a face measures 14 cm. What is the length of an edge of the cube? Round to the nearest tenth of a centimeter.

Answer 1

The side of the edge of the cube is 9. 9cm

How to determine the length

Given that the diagonal of a cube measures the square root of 294cm and the diagonal of a face measures 14cm

To find the edge of the face, we know that the face of the cube is a square

Formula for diagonal of a square = $\sqrt{2a}$

Where is the side of the square

We then have,

$\sqrt{2a} = 14$

Make 'a' the subject

a = $\frac{14}{\sqrt{2} }$

Simplify the surd

a = $\frac{14}{\sqrt{2} }$ × $\frac{14}{\sqrt{2} }$

a = $\frac{14\sqrt{2} }{2}$

a = $7\sqrt{2}$

a = 9. 9cm

Therefore, the side of the edge of the cube is 9. 9cm

Learn more about a cube here:

brainly.com/question/1972490

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