Question

Assertion (A): If the curved surface area of a right circular cylinder of height 14 cm is $$88\ \mathrm{cm}^{2}$$ then the diameter of its circular base is 2 cm.

Reason (R): Curved surface area of a right circular cylinder = area of circular base × height.

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. For a cylinder, $$2\pi rh = 88$$. With $$h = 14\ \mathrm{cm}$$ and $$\pi = \frac{22}{7}$$, this gives $$r = 1\ \mathrm{cm}$$, so the diameter is $$2\ \mathrm{cm}$$.

Step 2 – Reason: R is false. Curved surface area is circumference of the base multiplied by height, not area of the base multiplied by height. The latter gives the cylinder’s volume.

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