Question

The radii of two right circular cylinders are in the ratio 3:2 and their heights are in the ratio 5:3 . Calculate the ratio of their curved surface areas.​

Answer 1

Given :

• The radii of two right circular cylinders are in the ratio 3:2 and their heights are in the ratio 5:3.

To Find :

• Ratio of their Curved Surface Areas of cylinder = ?

Solution :

The CSA of a cylinder can be found with the following formula:

• CSA of cylinder = 2πrh

Where "r" is the radius and "h" is the height of the cylinder.

In this case, let be:

• r₁ the radius of the first one and r₂ the radius of the other cylinder.
• h₁ the height of one of them and h₂ the height of the other cylinder.
• CSA₁ the CSA of one of this cylinders and the CSA₂ of the other one.

Then,

⟶ CSA₁ = 2πr₁h₁

⟶ CSA₂ = 2πr₂h₂

Therefore,

➻ CSA₁ ÷ CSA₂ = 2πr₁h₁ ÷ 2πr₂h₂

By simplifying we get :

➻ CSA₁ ÷ CSA₂ = r₁h₁ ÷ r₂h₂

Now, knowing the ratios given in the question, you can substitute them into the equation:

→ CSA₁ ÷ CSA₂ = 3 × 5 ÷ 2 × 3

→ CSA₁ ÷ CSA₂ = 15 ÷ 6

→ CSA₁ ÷ CSA₂ = 15 ÷ 6

→ CSA₁ ÷ CSA₂ = 5 ÷ 2

⛬ Ratio of their Curved Surface Areas of cylinder is 5 : 2.