Calculus Related Rates:

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.

The snowball is a spherical figure and the surface area of the ball is calculated through the equation,

S = πD²

where S is surface area and r is the radius. Differentiating the equation gives,

dS/dt = 2πD (dD/dt)

Substituting the given,

7 = 2π (10) (dD/dt)

The value of dD/dt from the given equation is 0.11 cm/min.