Question

A cone, a hemisphere and a cylinder stand on equal basis and have the same height. Find the ration of their volumes.​

Answer 1

Answer:

1:2:3

Step-by-step explanation:

A cone, a hemisphere, and a cylinder stand on equal bases.

Hence radius of base of cone = radius of hemisphere = radius of cylinder=r

And,

They also have same height =h

Hight of cone =h

Hight of cylinder=h

Hight of Hemisphere r=h (r is the radius of sphere)

Now,

Volume of cone V c = 1 /3πr 2h...….(1)

Volume of hemisphere V h= 32 πr 2h×r = 2 /3πr 2 ×h

Vh = 2 /3πr 2 h…….(2)

Volume of cylinder V c =3/3πr 2 h...…..(3)

From equation 1,2 and 3

Vc:Vh:Vc= 1/3πr2h:2/3πr2h: 3/3πr2h

V c :V h :V c= 3:1 : 3:2 :1

V c :V h:VVc =1:2:3