Question

A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the radius is 17 cm. (Note the answer is a positive number).

Answer 1

Answer:

The volume of spherical snow ball is decreasing at a rate 1088.952 cubic cm per minute.

Step-by-step explanation:

We are given the following in the question:

The radius of a melting snowball is decreasing.

$\dfrac{dr}{dt} = -0.3\text{ cm per min}$

Instant radius = 17 cm

Volume of spherical snow ball =

$V=\dfrac{4}{3}\pi r^3$

Rate of change of volume =

$=\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt} = 4\pi r^2\times \dfrac{dr}{dt}\\\\\dfrac{dV}{dt} = 4(3.14)(17)^2\times (-0.3)\\\\\text{Negative sign shows decrease in volume}\\\\\dfrac{dV}{dt} = -1088.952\text{ cubic cm per min}$

Thus, the volume of spherical snow ball is decreasing at a rate 1088.952 cubic cm per minute.