The total surface area of a cylinder is 462 cm2. Its curved surface ar

1.	The total surface area of a cylinder is 462 cm2. Its curved surface area is one third of its total surface area. Find the volume of the cylinder.
Answer» We know that Curved surface area = 1/3 × Total surface area By substituting the values Curved surface area = 1/3 × 462 So we get Curved surface area = 154 cm² So the total surface area – curved surface area = 462 – 154 = 308cm² We know that 2 πr² = 308 By substituting the values 2 × (22/7) × r² = 308 On further calculation r² = (308 × 7)/44 So we get r² = 49 By taking square root r = √49 = 7cm We know that Curved surface area = 2 πrh By substituting the values 154 = 2 × (22/7) × 7 × h So we get h = 154/44 By division h = 3.5 cm So we get r = 7cm and h = 3.5 cm We know that Volume of the cylinder = πr²h By substituting the values Volume of cylinder = (22/7) × (7)² × 3.5 So we get Volume of cylinder = 539 cm³ Therefore, volume of the cylinder is 539 cm³.

The total surface area of a cylinder is 462 cm2. Its curved surface area is one third of its total surface area. Find the volume of the cylinder.

Answer»

We know that

Curved surface area = 1/3 × Total surface area

By substituting the values

Curved surface area = 1/3 × 462

So we get

Curved surface area = 154 cm²

So the total surface area – curved surface area = 462 – 154 = 308cm²

We know that

2 πr² = 308

By substituting the values

2 × (22/7) × r² = 308

On further calculation

r² = (308 × 7)/44

So we get

r² = 49

By taking square root

r = √49 = 7cm

We know that

Curved surface area = 2 πrh

By substituting the values

154 = 2 × (22/7) × 7 × h

So we get

h = 154/44

By division

h = 3.5 cm

So we get r = 7cm and h = 3.5 cm

We know that

Volume of the cylinder = πr²h

By substituting the values

Volume of cylinder = (22/7) × (7)² × 3.5

So we get

Volume of cylinder = 539 cm³

Therefore, volume of the cylinder is 539 cm³.