Question

1. the space diagonal of a cube is measured as $20\sqrt{3}$ cm. what is the side length of the cube?

a. 25 cm

b. 10 cm

c. 30 cm

d. 20 cm

Explanation:

Step1: Recall cube space diagonal formula

For a cube with side length $s$, the space diagonal $d$ is given by $d = s\sqrt{3}$.

Step2: Substitute given diagonal value

We know $d = 20\sqrt{3}$, so:
$$20\sqrt{3} = s\sqrt{3}$$

Step3: Solve for side length $s$

Divide both sides by $\sqrt{3}$:
$$s = \frac{20\sqrt{3}}{\sqrt{3}} = 20$$

Answer:

d. 20 cm