Question

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.

Answer 1

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.