so volume of a cone=[tex]\frac{1}{3} \pi r^2h[/tex]
where r is the radius of the cone
h is the height of the cone
and volume of a cylinder=[tex]\pi r'^2h' [/tex]
where r' is the radius of the cylinder
h' is the height of the cylinder
so as [tex] \frac{r'}{r}= \frac{3}{4}, \frac{h'}{h}= \frac{2}{3} [/tex]
So ratio of
[tex] \frac{Volumeofcylinder}{Volumeofcone} [/tex]
[tex]=\frac{\pi r'^2h'}{\frac{1}{3} \pi r^2h}[/tex] (π on above and below i cancelled)
[tex]=3( \frac{r'}{r} )^2( \frac{h'}{h} )= 3( \frac{3}{4} )^2( \frac{2}{3} )[/tex]
(1/(1/3)=3)(3²=9,4²=16)
[tex]= 3\frac{9}{16} (\frac{2}{3})=3( \frac{3}{16} )2[/tex]
3 above and below are cancelled
and then 16/2=8
[tex]=3\frac{3}{8}=\frac{9}{8}[/tex]
