Q. 54.4( 12 Votes )
A cylinder, a cone and a hemisphere of the equal base have the same height. What is their ratio in their volumes?
Given: radius of cone = radius of hemisphere = radius of cylinder = r
Height of cone = height of hemisphere = height of cylinder = h
To find: Ratio of volumes of given shapes.
Volume of the cone =
Volume of the hemisphere =
Volume of the cylinder = πr2h
Explanation: Since the cylinder, cone and the hemisphere have equal bases and equal height.
So, let the radius of the base be r and height be h.
∴ The volume of the cone, V1=
The volume of the hemisphere, V2 =
Volume of the cylinder, V3= πr2h
We know that the radius of base and height of hemisphere are equal.
r = h
Also a cylinder, a cone and a hemisphere have an equal base and have the same height
∴ The volume of the cylinder, V3 =
The ratio of their volumes = V1 : V2 : V3
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