Question

g If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at which the diameter decreases when the diameter is 8 cm.

Answer 1

0.0398cm/s

Explanation:

The snow ball is spherical in nature.

Total surface area of the spherical ball = 4πr²

= 4π(d/2)²

= 4π(d²/4)

= πd²

S = πd²

dS/dt = dS/dd • dd/dt

dS/dt = 2πd•dd/dt

Given

dS/dt = 2cm²/min

d = 8cm

Substitute and get dd/dt

2 = 2π(8) •dd/dt

2 = 16π•dd/dt

dd/dt = 2/16π

dd/dt = 1/8π

dd/dt = 1/8(3.14)

dd/dt = 1/25.12

dd/dt = 0.0398cm/s

Hence the rate at which the diameter is decreasing is 0.0398cm/s