Question

Assertion :Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm². Reason: If r be the radius and h be the height of the cylinder, then total surface area =(2πrh+2πr²)

A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct

Answer 1

The assertion about the total surface area of a cylinder with a base radius of 14 cm and height of 30 cm being 3872 cm² is incorrect; the correct calculation using the formula for total surface area results in 3864 cm². The reason provided is the correct formula for total surface area of a cylinder. Option D is the correct answer.

Step-by-step explanation:

The question involves using the formula for the total surface area of a cylinder to verify an assertion about the surface area of a particular cylinder with given dimensions. Given the radius (r) and height (h) of a cylinder, the formula for total surface area is 2πrh + 2πr². To verify the assertion, we plug in the values r = 14 cm and h = 30 cm into the formula:

Total Surface Area = 2π(14 cm)(30 cm) + 2π(14 cm)² = 2(3.14)(14 cm)(30 cm) + 2(3.14)(14 cm)² = 2632 cm² + 1232 cm² = 3864 cm².

The assertion is slightly incorrect because the calculated total surface area is 3864 cm², not 3872 cm². The reason given in the question is indeed the correct formula for the total surface area of a cylinder. Therefore, the correct option is D. Assertion is incorrect but Reason is correct.