Question

Assertion :When a sphere is cut along the diameter into two hemispheres, the total surface area increases. Reason: Total surface area of a hemisphere is equal to the addition of the curved surface area of the hemisphere and the area of circle of same radius.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Surface area of sphere$=4\pi r^2$

After cutting along the diameter, then

$TSA=2\pi r^2+\pi r^2=3\pi r^2$

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

Hence, TSA will be increased.

Therefore, option A is correct.