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A cone, cylinder, and hemisphere have the same base and the height of the cylinder is double the height of the hemisphere, but half of the height of the cone. Find the ratio of the volumes of the cone to the cylinder to the hemisphere?

A cone, cylinder, and hemisphere have the same base and the height of the cylinder is double the height of the hemisphere, but half of the height of the cone. Find the ratio of the volumes of the cone to the cylinder to the hemisphere? Correct Answer 4 ∶ 6 ∶ 2

Given:

Radius of a cone = radius of a Cylinder = radius of a hemisphere

Height of the cylinder = 2 × radius of the hemisphere

Height of the cone = 2 × height of the cylinder

Formula used:

Volume of cone = (1/3)πr2h

Volume of cylinder = πr2h

Volume of hemisphere = (2/3)πr3

Calculation:

Let, Height of hemisphere or radius of the hemisphere be r

Radius of cone = radius of Cylinder = radius of hemisphere = r

Height of cylinder = 2r

Height of cone = 4r

The volume of cone ∶ Volume of cylinder ∶ Volume of the hemisphere

= (1/3)πr2h ∶ πr2h ∶ (2/3)πr3

= ∶ ∶

= (4/3) ∶ 2 ∶ (2/3)

= 4 ∶ 6 ∶ 2

∴ The ratio of the volumes of the cone to cylinder to hemisphere is 4 ∶ 6 ∶ 2.

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