Question

The radii of the bases of a cylinder and a cone are in the ratio of 3:4 and their heights are in the ratio 2:3.Find the ratio of their volumes.

Answer 1

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

Answer 2

Answer:

hope it's correct

the answer is attached to the picture