Question

The surface area of a solid hemisphere with radius $r$ is

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

Answer 1

Answer: (C)

$3\pi r^2$

Surface area of a solid sphere with radius $r$ is $4\pi r^2$
A solid sphere can be divided into two equal hemispheres with a flat surface and a curved surface.
Curved surface area of a solid hemisphere will be half the surface area of solid sphere.
Hence, curved surface area of solid hemisphere $=\frac{1}{2}\ast 4\pi r^2=2\pi r^2$
And, flat surface area of hemisphere will be the area of circle with radius $r$.
Hence, flat surface area of hemisphere $=\pi r^2$
Total surface area of a solid hemisphere with radius $r$ is, $S=2\pi r^2+\pi r^2=3\pi r^2$