Question

A cube whose edge is 20 cm long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube if the circles are of the largest possible areas?

Options

• 90.72 cm²

• 256.72 cm²

• 330.3 cm²

• 514.28 cm²

Answer 1

514.28 cm² 

Explanation:

Diameter of largest circle = 20 cm.

∴ Area of circle = 100 π cm²

∴ Area of 6 circles = 6 × 100 π = 600π cm² (∵ there are six faces in a cube)

Also, Area of cube = 6 × (20)² = 2400 cm²

Area of unpainted surface = 2400 – 600π
= 2400 – 600 × `22/7`

= 514.28 cm²