(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A snowball melts such that the volume decreases at a rate of 1cm^{3}/min. At what rate is the diameter decreasing when diameter=10?

I know the answer is [itex]\frac{-1cm}{50∏ per ?}[/itex]. My problem is with the units on the bottom. It was given as seconds, but shouldn't it be per minute? There was no conversion done anywhere in the problem. The answer is small, and it seems like it would fit better as per seconds rather than per minute, but I can't find out how we went from minutes to seconds.

d=derivative

D=diameter

volume = [itex]\frac{4∏r^3}{3} = \frac{4∏(\frac{D}{2})^3}{3} = \frac{∏}{6}D^3[/itex]

[itex]\frac{dv}{dt}=\frac{-1cm^3}{min}=-1[/itex]

[itex]\frac{dv}{dt} = \frac{∏}{6}(3D^2)\frac{dD}{dt}[/itex]

[itex]-1 = \frac{∏}{6}(3D^2)\frac{dD}{dt}[/itex]

[itex]-1 = (\frac{D^2∏}{2})(\frac{dD}{dt})[/itex]

[itex]\frac{dD}{dt} = \frac{-1}{(D^2∏)/2}[/itex]

[itex]\frac{dD}{dt} = \frac{-2}{D^2∏}[/itex]

[itex]\left. \frac{dD}{dt}\right|_{D = 10} = \frac{-2}{(10)^2∏} = \frac{-2}{100∏} = \frac{-1}{50∏}[/itex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Related rates, simple question

**Physics Forums | Science Articles, Homework Help, Discussion**