# rate change word problem

• Mar 11th 2010, 05:26 PM
ascendancy523
rate change word problem
So I'm having trouble starting this problem.

A spherical snowball is melting in such a way that its radius is decreasing at the rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 8 cm?

Any suggestions?
• Mar 11th 2010, 06:34 PM
sa-ri-ga-ma
Volume of the sphere V = 4/3*π*r^3
dV/dt = 4/3*π*3*r^2*dr/dt.
Substitute the values to get the result.
• Mar 11th 2010, 11:10 PM
PeltierC
Quote:

Originally Posted by sa-ri-ga-ma
Volume of the sphere V = 4/3*π*r^3
dV/dt = 4/3*π*3*r^2*dr/dt.
Substitute the values to get the result.

You're right for sure, but this is under Geometry, and dv/dt is a Calculus concept!
• Mar 12th 2010, 01:59 AM
sa-ri-ga-ma
Quote:

Originally Posted by PeltierC
You're right for sure, but this is under Geometry, and dv/dt is a Calculus concept!

Then you can do this way.
Vf - Vi = ΔV = 4/3*π*[ (R+ΔR)^3 -R^3]
Using the factorization of (a^3 - b^3) simplify the above equation. Then find ΔV/Δt.