A cone-shaped icicle is dripping from the roof. The radius

[jesslup]

A cone-shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate of .2 cemtimeter per hour, while the length is increasing at a rate of .8 centimeter per hour. If the icicle is currently 4 centimeters in radius and 20 centimeters long, is the volume of the icicle increasing or decreasing, and at what rate?

 

[mammothrob]

a good place to start is with an equation/formula that describes a right cicular cone that uses the variables of radius and length/height.

Then try differentiating that...

(you gotta love those related rates problems)

 

[galactus]

\(\displaystyle \L\\V=\frac{1}{3}{\pi}r^{2}h\)

\(\displaystyle \L\\\frac{dV}{dt}=\frac{1}{3}{\pi}r^{2}\frac{dh}{dt}+\frac{2}{3}{\pi}r\frac{dr}{dt}h\)

\(\displaystyle =\L\\\frac{1}{3}{\pi}r(r\frac{dh}{dt}+2h\frac{dr}{dt})\)