Calculus
posted by Helga on .
A right circular cone has a constant volume. The height h and the base radius r can both vary. Find the rate at which h is changing with respect to r at the instant when r and h are equal.

v = pi/3 r^2 h
since v is a constant, dv = 0
0 = 2rh dr + r^2 dh
When r=h,
2r^2 dr + r^2 dh = 0
2dr + dh = 0
dh = 2dr
dh/dr = 2