Question

5. The ratio between the curved surface area
and the total surface area of a cylinder is
1:2. Find the ratio between the height and the
radius of the cylinder​

Answer 1

Question ⤵

$\rightarrow$ The ratio between the curved surface area and the total surface area of a cylinder is 1:2.

Find the ratio between the height and the radius of the cylinder

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To Find ⤵

$\rightarrow$The ratio between the height and the radius of the cylinder?

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Given ⤵

$\rightarrow$ CSA of Cylinder : TSA of Cylinder = 1:2

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Solution ⤵

$\rightarrow$CSA of Cylinder : TSA of Cylinder

$\frac{2\pi rh}{2πr(r+h) }$ = 1/2

$\frac{h}{r+h}$ = 1/2

_____________×_____________

$\rightarrow$By Cross Multiplication, We Get

2h = r+h

2h-h = r

$\because$ h = r

By Calculating, We Get Height Is Equal To Radius.

$\rightarrow$ Ratio of Their Height And Radius is

$\rightarrow$ Height of Cylinder : Radius of Cylinder = 1:1

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Answer 2

Let r be the radius and h be the height of a right circular cylinder, then Curved surface area = 2πrh

and total surface area = 2πrh x 2πr2 = 2πr(h + r)

But their ratio is 1 : 2

∴ 2πr/2πr(h + r) = 1/2 ⇒ h/(h + r) = 1/2

⇒ 2h = h + r ⇒ 2h – h = r

⇒ h = r = 1 : 1

Hence their radius and height area equal.