Question

The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular

faces is twice the area of the curved surface. Find the volume of the cylinder.​

Answer 1

Given :

The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular  faces is twice the area of the curved surface.

To find :

Find the volume of the cylinder.​

Solution :

Height of cylinder, h = 10.5 m

✢ Area of one circular face = πr²

∴ Sum of areas of two circular faces = 2πr²

✢ CSA of cylinder = 2πrh

Now atq,

⇒ 3(2πr²) = 2(2πrh)

⇒ 6πr² = 4πr(10.5)

⇒ 3r² = 2r × 10.5            [∵ Dividing both sides by '2π']

⇒ 3r² = 21r

⇒ 3r = 21            [∵ Dividing both sides by 'r']

⇒ r = 21/3

⇒ r = 7 m

✢ Volume of cylinder = πr²h

⇒ Volume of cylinder = 22/7 × (7)² × 10.5

⇒ Volume of cylinder = 22 × 7 × 10.5

⇒ Volume of cylinder = 1617 m³

∴ The volume of cylinder = 1617 m³

Answer 2

Answer:

Given :-

• Height of right circular cylinder = 10.5 m
• Three times the sum of the areas of its two circular faces is twice the area of the curved surface

To Find :-

Volume

Solution :-

Area of two circular face = 2 + πr² = 2πr²

CSA = 2πrh

3(2πr²) = 2(πr × 10.5)

6πr² = 4πr × 10.5

3πr² = 2πr × 10.5

3r² = 2r × 10.5

3r² = 21r

3r = 21

r = 21/3

r = 7

Now,

Volume = πr²h

Volume = 22/7 × 7² × 10.5

Volume = 22/7 × 49 × 10.5

Volume = 22 × 7 × 10.5

Volume = 1617 m³