The radius of a circle is increasing uniformly at the rate of 3 cm/s. What is the rate of increase of its area when the radius is 10 cm?

The radius of a circle is increasing uniformly at the rate of 3 cm/s. What is the rate of increase of its area when the radius is 10 cm?

• A. 60π cm²/s
• B. 30π cm²/s
• C. 100π cm²/s
• D. 60 cm²/s

Answer: A) 60π cm²/s

Explanation: Let r be radius and A be area. A = πr². Differentiating w.r.t t: dA/dt = 2πr(dr/dt). Given dr/dt = 3. When r = 10, dA/dt = 2π(10)(3) = 60π cm²/s.