Question

The ratio of the radii of two right circular cylinders is 1 : 2 and the ratio of their heights is 4 : 1. The ratio of their volumes is ______


No spams..❌❌​

Answer 1

Answer:-

1 : 1

Explanation:-

Given:-

• Ratio of radii of the cylinders = 1 : 2

• Ratio of heights of the cylinders = 4 : 1

To find:-

• Ratio of volumes of the cylinders

Solution:-

Let the radii of the cylinders be r and 2r and their heights be 4h and h respectively.

Also let the volume of the cylinders be V₁ and V₂ respectively.

• Volume of a cylinder = πr²h

Volume of 1st cylinder :-

=> V₁ = π × (r)² × 4h

=> V₁ = 4πr²h. ----(1)

Volume of 2nd cylinder :-

=> V₂ = π × (2r)² × h

=> V₂ = 4πr²h. ----(2)

Now, we will divide eq.1 by eq.2, to get the ratio of their volumes :-

=> V₁ / V₂ = 4πr²h/4πr²h

=> V₁ / V₂ = 1/1

=> V₁ : V₂ = 1 : 1

Thus, ratio of their volumes is 1 : 1 .

Answer 2

Answer:-

1 : 1

Explanation:-

Given:-

• Ratio of radii of the cylinders = 1 : 2

• Ratio of heights of the cylinders = 4 : 1

To find:-

• Ratio of volumes of the cylinders

Solution:-

Let the radii of the cylinders be r and 2r and their heights be 4h and h respectively.

Also let the volume of the cylinders be V₁ and V₂ respectively.

• Volume of a cylinder = πr²h

Volume of 1st cylinder :-

=> V₁ = π × (r)² × 4h

=> V₁ = 4πr²h. ----(1)

Volume of 2nd cylinder :-

=> V₂ = π × (2r)² × h

=> V₂ = 4πr²h. ----(2)

Now, we will divide eq.1 by eq.2, to get the ratio of their volumes :-

=> V₁ / V₂ = 4πr²h/4πr²h

=> V₁ / V₂ = 1/1

=> V₁ : V₂ = 1 : 1

Thus, ratio of their volumes is 1 : 1 .