If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm. (Give your answer correct to 4 decimal places.)

Answer 1

SA = 4πr^2
d(SA)/dt = 8πr dr/dt
when r = 4.5

3 = 8π(4.5) dr/dt
dr/dt = 3/(36π) cm/min

d(diameter)/dt = 2(3/(36π)) cm/min
= 1/(6π) cm/min or appr. 0.0531 cm/min

Answer 2

45.3434