Question

Assertion (A): The volume of a right circular cone whose area of the base is $$156\ \mathrm{cm}^{2}$$ and the vertical height is 8 cm, is $$416\ \mathrm{cm}^{3}$$.

Reason (R): If the radius and height of a cone are doubled then its volume becomes four times.

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 volume is: $$V = \frac{1}{3}\times156\times8 = 416\ \mathrm{cm}^{3}$$

Step 2 – Reason: R is false. Doubling the radius and height multiplies the volume by $$2^{2}\times2 = 8$$, not four.

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