Question

if the ratio of volumes of right circular cylinder and a cone is 3:2 then find tatio of their heights

Answer 1

let R and H is the radius and height of cylinder also r and h are radius and height of cone.
given,
volume of cylinder/volume of cone =3/2

πR^2H/(πr^2h/3)=3/2

R^2H/r^2h=1/2

if radius of cylinder =radius of cone
e.g. R=r
then
H/h=1/2

Answer 2

Let R and H is the radius and height of cylinder
 r and h are radius and height of cone.

Volume of cylinder/volume of cone =3/2

πR²H/(πr²h/3)=3/2

R²H/r²h=1/2

radius of cylinder =radius of cone
So the radii will cancel out each other

H/h=1/2

∴ The ratio is 1:2