F3 MAths Problems

1) Figure3 shows a cone of height 12cm and radius 3 cm for holding ice-cream. The ice-cream above the cone is in the shape of a hemisphere. There is an cone-shaped empty space at the bottom with a height of h cm.
(a) Find the capacity of the cone.

the capacity of the cone
=(1/3)πr²h
=(1/3)(3)²(12)π
=36π cm²

(b) Find the volume of the ice-cream above the cone.

the volume of the ice-cream above the cone
=(1/2)(4/3)πr³
=(2/3)(3)³π
=6π cm²

(c) When the ice-cream melts, it occupies the whole cone without any leakage. Find h

r₁/r=h/12
r₁=hr/12
=h/4 cm

6π=(1/3)πr₁²h

18=r₁²h
18=(h/4)²h
h³=288
h=³√288
=2³√36
=6.60 cm


2015-04-10 21:10:17 補充：
a,b or c？？

2015-04-11 10:43:24 補充：
(b) Find the volume of the ice-cream above the cone.

the volume of the ice-cream above the cone
=(1/2)(4/3)πr³
=(2/3)(3)³π
=(2)(3)²π
=18π cm²

I have the answer which is 18 π(cm^2) but I don't know the steps, plz help me.

2015-04-11 09:43:33 補充：
the question b