 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from Barbara, a student: Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s. |
Hi Barbara,
The volume of a cone of radius r cm and height h cm is given by
V = 1/3 π r2 h.
V, r and h are all functions of time and you are told that dr/dt = dh/dt = 2 cm/s. What you want is dV/dt when r = 10 cm and h = 20 cm.
Differentiate V = 1/3 π r2 h implicitly with respect to t and you will see that you know the value of each of the variables except dV/dt. Solve for dV/dt.
Harley
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.