Question

if the volume of a cone is increasing at a constant rate, is the height also increasing at a constant rate?

Answer 1

Not constant

Explanation:

We are supposed to find if the rate of increase of height is constant or not when the rate of increase of volume is constant.

Given object is cone , which has the volume height relation as

`V=(1)/(2)\pi  r^2h`

when we differentiate this equation ,

`(dv)/(dt)=(1)/(2)\pi   (2r(dr)/(dt)h+r^2(dh)/(dt)  )`

here we observe that though
`(dv)/(dt)` is constant the rate of change of height is dependent on r and h so its not constant.