A perfect cube with a side length of 8 cm has the largest…

A perfect cube with a side length of 8 cm has the largest possible sphere fitted inside it. What is the volume of the empty space within the cube?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 512 - $\frac{256\pi}{3}$ cm³.

Cube side = 8 cm

Volume of a cube = (8)³ = 512 cm³

Largest sphere inside cube ⇒ diameter = 8 cm

Radius = 4 cm

Volume of sphere = $4\over3$ πr³ = $4\over3$ π × (4)³ = $256π\over3$ cm³

Empty space = 512 − $256π\over3$ cm³

SSC CGL 2025 PYQ — Question 71