Question

The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm square . find the valume of the cylinder.​

Answer 1

A N S W E R :

It is given that,the sum of the height and the radius of a solid cylinder is 35 cm, mathematically it can be expressed as :

• r + h = 35

[ Where, r is the radius of solid cylinder and h is the height of solid cylinder ]

First of all we need to find the radius and height of the solid cylinder :

→ Total surface area of cylinder = 2πr(r + h)

→ 3080 = 2 × 22/7 × r × 35

→ 3080 = 2 × 22 × 5 × r

→ 3080 ÷ 44 = 5r

→ 70 = 5r

→ r = 70 ÷ 5

→ r = 14 cm

Hence,the radius of solid cylinder is 14 cm.

Let's find the height of the cylinder :

→ r + h = 35

→ 14 + h = 35

→ h = 35 - 14

→ h = 21 cm

• Hence,the height of solid cylinder is 21 cm.

Now, calculate the volume of cylinder :

→ Volume of cylinder = πr²h

→ Volume of cylinder = 22/7 × (14)² × 21

→ Volume of cylinder = 22 × 2 × 14 × 21

→ Volume of cylinder = 12,936 cm³

• Hence,the volume of cylinder is 12,936 cm³.