Question

Assertion (A): The curved surface area of a cone having height 24 cm and radius 7 cm is $$550\ \mathrm{cm}^{2}$$.

Reason (R): The curved surface area of a cone is given by $$S = 2\pi rh$$, where $$r$$ and $$h$$ denote the radius of the base and height of the cone respectively.

Options

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

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. The cone’s slant height is $$l = \sqrt{7^{2} + 24^{2}} = 25\ \mathrm{cm}$$, so its curved surface area is $$\pi rl = \frac{22}{7}\times7\times25 = 550\ \mathrm{cm}^{2}$$.

Step 2 – Reason: R is false. The formula as given in the question is not the cone’s curved surface area formula; the correct formula is $$\pi rl$$.

Therefore, the correct option is: Assertion (A) is true and Reason (R) is false.