Thread: Related Rates Involving A Cone

A cone is 40 cm in height and 20 cm in diameter at widest point. If it is being filled at a rate of 10pi mL/min, how fast is its height changing when it is half filled?

So far, I've got that r/h = 1/4, so r = h/4.

And I've got that dV/dt = pi/48 x 3h^2 x dh/dt

However, I'm stumped on how to find the height when the cone is half filled.

Any help is appreciated.

Originally Posted by Shapeshift

A cone is 40 cm in height and 20 cm in diameter at widest point. If it is being filled at a rate of 10pi mL/min, how fast is its height changing when it is half filled?

So far, I've got that r/h = 1/4, so r = h/4.

And I've got that dV/dt = pi/48 x 3h^2 x dh/dt

However, I'm stumped on how to find the height when the cone is half filled.

Any help is appreciated.

volume of full cone ...

half full ...

Originally Posted by Shapeshift

A cone is 40 cm in height and 20 cm in diameter at widest point. If it is being filled at a rate of 10pi mL/min, how fast is its height changing when it is half filled?

So far, I've got that r/h = 1/4, so r = h/4.

And I've got that dV/dt = pi/48 x 3h^2 x dh/dt

However, I'm stumped on how to find the height when the cone is half filled.

Any help is appreciated.

..

half filled means volume is halved.