Question

$If \: the \: ratio \: of \: the \: total \: surface \\ area \: of \: a \: cylinder \: to \: the \: curved \\ surface \: area \: of \: the \: cylinder \: is \\ 2:1, \: find \: the \: ratio \: of \: its \: radius \: to \\ its \: height.​$​

Answer 1

Answer:

given,

total surface area of cylinder = 2:1

2πrh / 2πr(r+h) = 2/1

h/(r+h) = 2/1

by cross multiplication, we get

2h = r+h

2h-h = r

therefore h=r

by calculating, we get height is equal to radius. then ratio of their height and radius is

height of cylinder : radius of cylinder = 1:1

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.

Step-by-step explanation:

Hope it helps you ✌️✌️