Question

if the radius of a cylinder is doubled keeping its lateral surface area the same then what is its hight​

Answer 1

Given:-

• L.S.A. of cylinder₁ = L.S.A. of cylinder₂

• 2 × Radius of cylinder₁ = Radius of cylinder₂

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To Find:-

• Changes in Height of cylinder

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Formula Used:-

• L.S.A. of cylinder = 2πrh

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Solution:-

Let the radius of cylinder₁ be r₁

And Radius of cylinder₂ be r₂

Let the Height of cylinder₁ be h₁

And Height of cylinder₂ be h₂

So,

• L.S.A. of cylinder of r₁ = 2πr₁h₁

• L.S.A. of cylinder of r₂ = 2πr₂h₂

• 2πr₁h₁= 2πr₂h₂

• r₂ = 2r₁

According to given conditions;

L.S.A. of cylinder₁ = L.S.A. of cylinder₂

➟ 2πr₁h₁ = 2πr₂h₂

➟ 2πr₁h₁ = 2π2r₁h₂

➟ h₁ = 2h₂

➟ h₂ = h₁ ÷ 2

Hence,

New Height is half of previous height.

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Here;

• L.S.A. = Lateral Surface Area
• r = Radius
• h = Height
• π = 22/7