The radius of a spherical balloon is increasing at the rate of 10 cm/s. Find the rate of change of its volume when the radius is 15 cm. A. 9000π cm³/s B. 4500π cm³/s C. 3000π cm³/s D. 900π cm³/s Answer: A) 9000π cm³/s Explanation: Volume V = (4/3)πr³. dV/dt = 4πr²(dr/dt). Given dr/dt = 10 and r = 15. dV/dt = 4π(15²)(10) = 4π(225)(10) = 9000π cm³/s.

imo class 12 application of derivatives

The radius of a spherical balloon is increasing at the rate of 10 cm/s. Find the rate of change of its volume when the radius is 15 cm.

VAVidaara Admin Asked 6d ago 0 views 0 answers

The radius of a spherical balloon is increasing at the rate of 10 cm/s. Find the rate of change of its volume when the radius is 15 cm.

Answer: A) 9000π cm³/s

Explanation: Volume V = (4/3)πr³. dV/dt = 4πr²(dr/dt). Given dr/dt = 10 and r = 15. dV/dt = 4π(15²)(10) = 4π(225)(10) = 9000π cm³/s.