Question

Assertion: The surface are of a sphere is 2464 cm². Its volume is $11498\frac{2}{3}{\mathrm{cm}}^3\left(\mathrm{\pi }=\frac{22}{7}\right).$
Reason: The volume of a sphere of radius r is $\frac{4}{3}{\mathrm{\pi r}}^3$.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.

$$\begin{gathered} \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{sphere}=4\mathrm{\pi }{r}^2=2464{\mathrm{cm}}^2 \\ \therefore r=\sqrt{\frac{2464\times 7}{4\times 22}}=14\mathrm{cm} \end{gathered}$$
$\mathrm{Now},\mathrm{its}\mathrm{volume}=\frac{4}{3}\mathrm{\pi }(14{)}^3=11498.66{\mathrm{cm}}^3=14988\frac{2}{3}{\mathrm{cm}}^3$
Reason (R) is clearly true.
Assertion (A) is true but reason (R) is not the correct explanation of assertion (A).