Homework Help: Math (Calculus)

Posted by Alex on Thursday, November 29, 2012 at 11:28pm.

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 10 cm.

Can someone help & explain how to solve this question? Please.

Math (Calculus) - Steve, Friday, November 30, 2012 at 12:10am
v = 4/3 pi r^3
dv/dt = 4pi r^2 dr/dt
= 4pi * 25cm^2 * -0.3cm/min
= -30pi cm^3/min
Math (Calculus) - Reiny, Friday, November 30, 2012 at 10:45am
small correction to Steve's solution

d(diameter)/dt = -.3
dr/dt = -.15

so dv/dt = 4π(25)(-.15) = -15π cm^3/min

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