Question

A diagonal of a cube measures StartRoot 150 EndRoot cm. The diagonal of a face measures 10 cm.

Answer 1

The side of the edge of the cube is 7. 07cm

How to determine the length

Given that a  diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.

Let's find the edge of the face

Note that the face of the cube is in the shape of square .

The diagonal of the face is 10 cm.

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

a is the side of the square face

We have that,

$\sqrt{2a} = 10$

Make 'a' subject of formula

a = $\frac{10}{\sqrt{2} }$

Find the surd of the equation, we have

a = $\frac{10}{\sqrt{2} }$ × $\frac{\sqrt{2} }{\sqrt{2} }$

a = $\frac{10\sqrt{2} }{2}$

a = $5\sqrt{2}$

a = $7. 07cm$

Thus, the side of the edge of the cube is 7. 07cm

Learn more about a cube here:

brainly.com/question/1972490

#SPJ1