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.

Answer 1

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