Question

Assertion (A): The area of canvas cloth required to just cover a heap of rice in the form of a cone of diameter 14 m and height 24 m is $175\pi$ sq.m.
Reason (R): The curved surface area of a cone of radius $r$ and slant height $l$ is $\pi r l$.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Answer 1

The Correct Option is A

Step 1: Verify Assertion (A):
The rice heap is conical, with a diameter of 14 m and a height of 24 m. The canvas needed is the cone's curved surface area.
Radius \( r = \frac{14}{2} = 7 \, \text{m} \).
Height \( h = 24 \, \text{m} \). The slant height \( l \) is calculated using the Pythagorean theorem: \( l = \sqrt{r^2 + h^2} \).
Substituting values: \( l = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \, \text{m} \).
Curved Surface Area = \( \pi r l \).
Substituting \( r \) and \( l \): Curved Surface Area = \( \pi \times 7 \times 25 = 175\pi \, \text{sq.m} \).
The assertion that \( 175\pi \) sq.m of canvas is required is correct.

Step 2: Verify Reason (R):
Reason (R) states the formula for the curved surface area of a cone is \( \text{Curved Surface Area} = \pi r l \), where \( r \) is the radius and \( l \) is the slant height. This formula is correct.

Step 3: Conclusion:
Both Assertion (A) and Reason (R) are true. Reason (R) accurately explains Assertion (A).
Therefore, the correct answer is:
\[ \boxed{\text{Both (A) and (R) are true, and (R) is the correct explanation of (A)}} \]