# 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. - Mathematics

Sum

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.

#### Solution

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

therefore (2pir)/(2pir(h + r)) = 1/2 ⇒ h/(h + r) = 1/2

⇒ 2h = h + r ⇒ 2h - h = r

⇒ h = r = 1 : 1

Hence their radius and height are equal

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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 21 Surface Area, Volume and Capacity
Exercise 21 (D) | Q 5 | Page 242