Question

What is the ratio of the volumes of a right circular cylinder , cone and hemisphere having same diameter and height

Answer 1

let V1 , V2 and V3 are the volumes of right circular cylinder ,cone and hemisphere.

since , diameter and hight of right circular cylinder , cone and of hemisphere are same.

then , their radius will also be same .

volume of right circular cylinder
V1 = πr^2h

volume of cone V2= πr^2h / 3

volume of hemisphere V3 = 2πr^3/ 3

since , the height of right circular cylinder, cone and hemisphere is same and they are on the same base , so then height of right circular cylinder and cone will be equal to radius of hemisphere.

h = r ( radius of hemisphere )

V1 = πr^2h = πr^2r = πr^3

V2 = πr2h / 3 = πr^3 / 3

V1 = 2πr^3 / 3

ratio of their volumes

V1 : V2 : V3 = πr^3 : πr3/ 3 : 2πr^3 / 3

V1 : V2 : V3 = 1 : 1/ 3 : 2/ 3

=3 : 1 : 2 or V2 : V3 : V1 = 1 : 2 : 3

therefore,

ratio of their volumes = 3 : 1 : 2

Your Answer : V1 : V2: V3 = 3 : 1 : 2
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