Question

Assertion :The volume and surface area of a sphere are related to each other by radius. Reason: The relaion between the Surface area $S$ and Volume $V$ is: $S^3=36\pi V^2$

• 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

Volume of sphere, $V=\frac{4}{3}\pi r^3\Rightarrow r={\left(\frac{3V}{4\pi }\right)}^{1/3}$

Surface area of sphere,$S=4\pi r^2=4\pi {\left(\frac{3V}{4\pi }\right)}^{2/3}$

$S^3=64{\pi }^3{\left(\frac{3V}{4\pi }\right)}^2=\frac{64{\pi }^2\times 9V^2}{16{\pi }^2}=36V^2$

$S^3=36V^2$

Hence, option A is correct