a cylinder , a cone and a hemisphere of equal base have the same height. what is their ratio in their volumes ?

Let r and h be the radius of base and height of the cylinder, cone and hemisphere.

We know that, Height of hemisphere = Radius of the hemisphere

h = r

Volume of cylinder = πr2h = πr2 × r = πr3

Volume of cone =  

Volume of hemisphere =

Volume of cylinder : Volume of cone : Volume of hemisphere

Thus, the ratio of their volumes is 3 : 1 : 2.

  • 180

 in case of the hemisphere,

radius= r

volume of d hemishpere= 2/33

in case of cylinder,

radius= r

height= r

volume= r2h= r3

in case of cone,

radiius= r

height= r

volume of the cone= 1/3r2h = 1/3r3

ratio of their volumes= r: 1/3r: 2/3r3

  =  1:1/3:2/3

  = 3:1:2

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