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.

Formula Used:

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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