Question

This one is kinda hard. "A ballon in the shape of a cylinder with hemispherical ends of the same radius as that of the cylinder is shown. The ballon is being inflated at the rate of 261pi cubic centimeters per minute. At the instant the radius of the cylinder is 3 centimeters, the volume of the ballon is 144pi cubic centimeters and the radius of the cylinder is increasing at the rate of 2 centimeters per minute. At this instant, how fast is the height of the entire ballon increasing?"

Answer 1

Write the volume equation as a function of radius..

v= PI*r*heightcyclinder + 4/3 PI r^3

Put numbers in...I don't see height in the problem given.

dV/dT= 261

When r=3, V= 144, and dr/dt= 2

Find dh/dt
dv/dt= PI*dr/dt*height + dh/dt*PI*r + 4PIr^2 dr/dt

you can find dh/dt here, once you solve for height in the volume equation

Answer 2

Thanks that kinda but not really helps me.