Answer:
0.0398cm/s
Step-by-step 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
