Thread: application

problem: A right circular cone expands in such a way that the altitude remains equal to the diameter of the base. Find the rate of the volume with respect to the radius of the base if the radius is equal to 5cm.

Originally Posted by cazimi

problem: A right circular cone expands in such a way that the altitude remains equal to the diameter of the base. Find the rate of the volume with respect to the radius of the base if the radius is equal to 5cm.

V = (1/3)(pi)r^2h

dV = (2/3)(pi)rh dr + (1/3)(pi)r^2 dh

Now
h = 2r

dh = 2dr

Thus
dV = (2/3)(pi)r(2r) dr + (1/3)(pi)r^2 * 2dr

dV/dr = (4/3)(pi)r^2 + (2/3)(pi)r^2

dV/dr = 2(pi)r^2

-Dan