Question

The radius of a solid sphere is $rcm$. It is bisected, then the total surface area of the two pieces obtained is:

• A. $8\pi r^{2}c{m}^2$
• B. $4\pi r^{2}c{m}^2$
• C. $5\pi r^{2}c{m}^2$
• D. $6\pi r^{2}c{m}^2$

Answer 1

The correct option is D $6\pi r^{2}c{m}^2$

Given, the radius of the sphere $=rcm$.

If the sphere is divided into two equal parts, then the resulting parts are hemispheres with radius $=rcm$.

Therefore, the total surface area of each hemisphere $=3\pi r^2$

Then, the total surface area of both hemisphere $=2\times 3\pi r^2=6\pi r^{2}c{m}^2$.

Hence, option $D$ is correct.