The total surface area of a solid cylinder is 231 cm2 and its curved

1.	The total surface area of a solid cylinder is 231 cm2 and its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.
Answer» We know that Curved surface area = 2/3 × Total surface area By substituting the values Curved surface area = 2/3 × 231 So we get Curved surface area = 154 cm² So the total surface area – curved surface area = 231 – 154 = 77cm² We know that 2 πr² = 77 By substituting the values 2 × (22/7) × r² = 77 On further calculation r² = (77 × 7)/44 So we get r² = 49/4 By taking square root r = √49/4 = 7/2cm We know that Curved surface area = 2 πrh By substituting the values 154 = 2 × (22/7) × (7/2) × h So we get h = 154/22 By division h = 7 cm So we get r = 7/2 cm and h = 7 cm We know that Volume of the cylinder = πr²h By substituting the values Volume of cylinder = (22/7) × (7/2)² × 7 So we get Volume of cylinder = 269.5 cm³ Therefore, volume of the cylinder is 269.5 cm³.

The total surface area of a solid cylinder is 231 cm2 and its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.

Answer»

We know that

Curved surface area = 2/3 × Total surface area

By substituting the values

Curved surface area = 2/3 × 231

So we get

Curved surface area = 154 cm²

So the total surface area – curved surface area = 231 – 154 = 77cm²

We know that

2 πr² = 77

By substituting the values

2 × (22/7) × r² = 77

On further calculation

r² = (77 × 7)/44

So we get

r² = 49/4

By taking square root

r = √49/4 = 7/2cm

We know that

Curved surface area = 2 πrh

By substituting the values

154 = 2 × (22/7) × (7/2) × h

So we get

h = 154/22

By division

h = 7 cm

So we get r = 7/2 cm and h = 7 cm

We know that

Volume of the cylinder = πr²h

By substituting the values

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

So we get

Volume of cylinder = 269.5 cm³

Therefore, volume of the cylinder is 269.5 cm³.