Question

Assertion(A) : The radius of a cylinder is doubled and its height remaining same. Then its volume will be increased four times.

Reason (R): Volume of the cylinder is $\pi r^{2}h$ where, r = radius of base and h = height of the cylinder.

• A. both Assertion and Reason are correct but Reason is not correct explanation for Assertion
• B. both Assertion and Reason are correct and Reason is correct explanation for Assertion
• C. both Assertion and Reason are false
• D. Assertion is correct but Reason is false

Answer 1

The correct option is B both Assertion and Reason are correct and Reason is correct explanation for Assertion

The correct option is (A). both Assertion and Reason are correct and Reason is correct explanation for Assertion

Consider:
r (old radius) and R (new radius)
v (old volume) and V (new volume)

As, v = $\pi r^{2}h$
R = 2r
V = $\pi R^{2}h$ {same height}
V = $\pi (2r{)}^{2}h$
V = 4$\pi r^{2}h$
V = 4v (Hence volume becomes 4
times on doubling radius)