Question

A spherical snowball is melting in such a way that its diameter is decreasing at a rate of 0.3cm per minute. At what rate in cubic cm per minute is the volume of the snowball changing when the diameter is 9cm? Submit an exact answer in terms of π. Do not forget to include a negative sign if the volume is decreasing. Hint: The volume of a sphere of radius r is V=43πr3.

Answer 1

Answer: The volume of the snowball changing at a rate of -12.15 cubic cm per minute

Explanation: Please see the attachments below

Answer 2

Answer: 12.15π cm³/min

Step-by-step explanation:

Given,

Diameter, d = 9 cm

Volume of a sphere, v = 4/3.π.r³

dD/dt = -0.3 cm/min (the negative sign is because it is decreasing)

Volume = 4/3.π.(d/2)³

Volume = 4/3.π.(d³/8)

Volume = 1/3.π.(d³/2)

Volume = 1/6.π.d³

dV/dt = 1/2.π.d².(dD/dt), substituting the value of dD/dt onto this, we have

dV/dt = 1/2.π.9².(-0.3)

dV/dt = 1/2.π.81.-0.3

dV/dt = 1/2.π.-24.3

dV/dt = -12.15π cm³/min

Thus, the volume of the snowball is changing at 12.15π cm³/min