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

$\huge \underline \pink {answer}$

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

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.