#### Question

A solid cylinder has total surface area of 462 cm2. Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.

#### Solution

We have

Curved surface area = `1/3` × total surface area

⇒ `2πrh = 1/3(2 πrh + 2πr^2)`

⇒ `6πrh = 2πrh +2πr^2`

⇒ `4πrh =2πr^2`

⇒ 2h = r

We know that,

Total surface area = 462

⇒ Curved surface Are = `1/3`× 462

2πrh =154

⇒ `2× 3.14× 2h^2 = 154`

⇒ `h^2=(154× 7)/(2× 22× 2)`

⇒ `49/4`

⇒ h=`7/2`cm

⇒ r=2h

⇒ r=`2× 7/2cm`

⇒ r=7cm.

Is there an error in this question or solution?

Solution A Solid Cylinder Has Total Surface Area of 462 Cm2. Its Curved Surface Area is One-third of Its Total Surface Area. Find the Radius and Height of the Cylinder. Concept: Surface Area of a Right Circular Cylinder.