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.
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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.
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