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

Answer:

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.

Answer 2

If the ratio between the curved surface area and the total surface area of a right circular cylinder is 1:3, then what is the ratio of the height and radius of the cylinder?

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Answered January 29

Curved surface area of a cylinder = 2πrh

And total surface area of a cylinder = 2πr(h + r)

The ratio given = 2πrh:2πr(h + r)=1:3

Or, 2πrh/2πr(h + r)=1/3

Or, h/(h + r)=1/3

Or, 3h = 1×(h+r) = h+r

Or, 3h - h = r

Or, 2h = r

Or, 2h/r = 1

Or, h/r = 1/2

Or, h:r = 1:2

Therefore, the ratio of the height and radius of the cylinder is 1:2.