Question

a cylinder a cone and a sphere have smae base diameter and height find the ratio of their volumes

Answer 1

vol of cylinder=πr^2h;vol of cone=1/3πr^2h;vol of a sphere=4/3πr^3.
same diameter=same radius =d/2
vol of cylinder:vol of cone: volume of sphere
πr^2h:1/3πr^2h:4/3πr^3
1:1/3:4/3r

Answer 2

Let volumes of cylinder, Cone, sphere be V1,V2,V3 resp.
Ratios of V1,V2,V3 is
πr2h: 1/3πr2h: 4/3πr3. •••••(I)
Given that- Solids have same radius and height.
Therefore,2r=h. •••••(ii)
Putting value of (ii) in (I)
We get,
2πr3: 2πr3/3: 4πr3/3=
6πr3/3: 2πr3/3; 4πr3/3=
6:2:4= 3:1:2
Hence the ratios are 3:1:2.