Question

g If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 12 cm. (Round your answer to three decimal places.)

Answer 1

Answer:

Rate of change of the diameter is equal to 0.053cm/min

Step-by-step explanation:

A snowball is of the shape of a sphere

Surface area of Sphere (S)= $4*pi*R^2$

Rate of change of surface area

dS/dt = -4$cm^2/min$

the negative sign indicates the surface area is decreasing.

Radius = d/2 where d represents diameter

using this is the surface area equation

S = $4*pi*(d/2)^2$

   = $pi*d^2$

dS/dt = 2*pi*d*d(d)/dt

4 = 2*pi*d*(d)/dt

d(d)/dt = 2/12*pi= $\frac{1}{6pi}$ cm/min

so the rate of change of the diameter is equal to 0.053cm/min