Question

Assertion: The base radius of a cone is 7 cm and its slant height is 25 cm. The volume of the cone is 1232 cm³.
Reason: The volume of a right circular cone of base radius r and height h is $\frac{1}{3}\mathrm{\pi }{r}^{2}h$.
(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

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Reason (R) is clearly true.
Let r cm be the radius of base of the cone .
$$\begin{gathered} \mathrm{Then}h=\sqrt{l^2-r^2}=\sqrt{{25}^2-7^2} \\ =\sqrt{625-49}=\sqrt{576}=24\mathrm{cm} \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24 \\ =1232{\mathrm{cm}}^3 \end{gathered}$$

Reason (R) and assertion (A) are both true and R is the correct explanation of A.
Hence, the correct option is (a).