A cone, cylinder, and hemisphere have the same base and the height of

1.	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?1. 3 ∶ 5 ∶ 22. 6 ∶ 4 ∶ 23. 4 ∶ 6 ∶ 24. 1 ∶ 3 ∶ 1
Answer» Correct Answer - Option 3 : 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 = [(1/3) × r² × 4r] ∶ [r² × 2r] ∶ [(2/3) × r³] = (4/3) ∶ 2 ∶ (2/3) = 4 ∶ 6 ∶ 2 ∴ The ratio of the volumes of the cone to cylinder to hemisphere is 4 ∶ 6 ∶ 2.

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?1. 3 ∶ 5 ∶ 22. 6 ∶ 4 ∶ 23. 4 ∶ 6 ∶ 24. 1 ∶ 3 ∶ 1

Answer» Correct Answer - Option 3 : 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

= [(1/3) × r² × 4r] ∶ [r² × 2r] ∶ [(2/3) × r³]

= (4/3) ∶ 2 ∶ (2/3)

= 4 ∶ 6 ∶ 2

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