Question

The radius of a solid sphere is $r$ cm. If 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 $6\pi r^{2}c{m}^2$

The area of a circle of radius r is $\pi r^2$

and thus if the hemisphere is meant to include the base then the surface area is $2\pi r^2+\pi r^2=3\pi r^2$. Hence in this case $3\pi r^2$ .

Then Surface area of two bisected sphere=$3\pi r^2+3\pi r^2=6\pi r^2$