If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.

D = 10 cm, r = 5 cm;

A = 4 r² π = 4 · 5² · 3.14 = 314 cm²

In one minute:

A 1 = 314 - 7 = 307 cm²

307 = 4 r 1² π

r 1² = 307: 12.56

r 1² = 24.44

r 1 = 4.944

d 1 = 2 · 4.944 = 9.888 cm

10 - 9.888 = 0.112

Answer:

The rate at which the diameter decreases is 0.112 cm / min.