Question

If the ratio of the radii of two cylinders is equal to the height of 1 : 3 find the ratio of their curved surface area

Answer 1

My dear friend,

We have given that, the ratio of the radii of two cylinder of equat height = 1:3

Find out their ratio of their curved surface area= ?

Let assume that, radii of first cylinder be = r1

Height of the cylinder = h1

Curved area surface of first cylinder A1= 2πr1h1—-(1)

Let assume that, radii of first cylinder be = r2

Height of the cylinder = h2

Curved area surface of first cylinder A2= 2πr2h2—-(2)

Now, A1/A2 = (2πr1h1)/(2πr2h2)

A1/A2= (r1/r2) × (h1/h2). (h1=h2)

A1/A2=(1/3) answer.

So their areas will be remained in same ratio of radii.

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Answer 2

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$\sf \: Let \: the \: radius \: of \: one \: cylinder \: be \: x \\ \sf \: And \: the \: other \: radius \: be \: 3x.$

Heights of both the cylinders are equal

$\sf \: CSA \: of \: cylinder = 2πrh$

$\sf \: C.S.A \: first \: cylinder : C.S.A \: of \: second \: cylinder$$\sf \: 2π \times x \times h : 2π \times 3x \times H$

$\sf \: x : 3x \\ 1:3$

The ratio of their CSA is 1 : 3