Question

A solid sphere of radius $r$ is sliced by the planes passing through its centre and perpendicular to each other. The total surface area of each of the pieces so formed is

• A. $\frac{2}{3}\pi r^2$
• B. $\pi r^2$
• C. $\frac{4}{3}\pi r^2$
• D. $2\pi r^2$

Answer 1

Answer: (D)

$2\pi r^2$

The surface of one piece consists of one-fourth of the surface area of the sphere and two semicircular areas
$\therefore$ Surface area of one piece
$=\frac{1}{4}.4\pi r^2+2.\frac{1}{2}\pi r^2=2\pi r^2$