Maths P1 Nov 2005 Q5(i)

[haris]

how can we prove this.............

 

[PlanetMaster]

First see the image in 2-Dimension just as it is in question.
Using similar triangles:
..r.....=...6.
12-h......12
So h =12−2r

Now come to 3-Dimension.
Vol of cylinder = πr²h
Vol of cylinder = πr²(12-2r)
Vol of cylinder = 12πr² - 2πr³ (Shown)