Question

Assertion :If the radius of a sphere is doubled, the surface area becomes four times the original surface area. Reason: Surface area of a sphere is proportional to the square of the radius of sphere.

• 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

Let initial radius of sphere be 'r', then its surface area,

$S=4\pi r^2\to 1$

New radius$=2r$ & new surface area,

$S^{\prime }=4\pi {\left(2r\right)}^2=4\pi \times 4r^2=4\times 4\pi r^2=4s$

Hence new surface area$=4$ times the old surface area

$\because S\propto r^2$

Hence both assertion and reason are correct and reason is the correct explanation for assertion.