How to find the maximum volume?

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

1 Answer
Dec 17, 2017

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