Question

How to solve using derivative??

A mat is carrying sand and pouring it into a cone. The radius of the base r = r (t) and the height h = h (t) vary over time. At the instant the height is 10 cm, it is increasing at a rate of 2cm / s, and at that moment the radius of the base is 12cm and is increasing at a rate of 1cm / s. Calculate the rate of change of cone volume at this point. `pi = 3`

Answer 1

We know the volume of a cone is given by `V = 1/3pir^2h`. Thus, taking the derivative with respect to time using the product rule, we should get

`(dV)/(dt) = 1/3pi(2r)h(dr)/(dt) + 1/3pir^2(dh)/(dt)`

`(dV)/(dt) = 1/3pi(2 * 12)(10)(1) + 1/3pi(12)^2(2)`

`(dV)/(dt) = 176pi` cubic centimeters per second

If `pi = 3`, then

`(dV)/(dt) = 528` cubic centimetres per second.

Hopefully this helps!