Question

A solid sphere with a radius of 4 cm is cut into 4 identical pieces by two mutually perpendicular planes passing through its centre. Find the total surface area of one-quarter piece.

Options

• 24π

• 32π

• 48π

• 64π

Answer 1

32π

Explanation:

Sphere area = 4πr².

The spherical curved part of one piece is one-quarter of that

= `1/4 xx 4π(4^2)`

= 16π 

Each cutting plane produces a semicircular flat face; there are two semicircles, whose combined area equals a full circle πr² = 16π.

Total surface area 

= 16π + 16π 

= 32π