Question

The increase in the total surface area of a sphere of Radius $R$ when it is cut to make two hemispheres of same Radius will be equal to:

• A. $5\pi R^2$
• B. $4\pi R^2$
• C. $3\pi R^2$
• D. $2\pi R^2$

Answer 1

The correct option is D $2\pi R^2$

Total surface area of sphere$=4\pi R^2$

TSA of hemisphere=CSA of hemisphere+CSA of circle

$=2\pi R^2+\pi R^2=3\pi R^2$

$\therefore$TSA of two hemisphere$=2\times 3\pi R^2=6\pi R^2$

Therefore, increase in TSA$=6\pi R^2-4\pi R^2=2\pi R^2$