Question

How to find the maximum volume?

Can someone please tell me where I went wrong with question 3b? I don't know why x has be 0<x<6? Thank!

Answer 1

See below,

Explanation:

For question 3b.

If `x` is the depth of water, then when the bowl is empty `x` will be 0. The maximum depth is the radius of the bowl i.e 6cm.

So `x` will be `0<=x<=6`

Volume when bowl is full will be when `x=6`

`V=1/3pi(6)^2(18-6)=144pi`

You can check by using the formula for the volume of a sphere:

`V = 4/3pir^3`

We need half the volume:

`1/2V=1/2(4/3pi(6)^3)=(288pi)/2=144pi`