Question

The height and radius of the cylinder is in the ratio of 7:5 and it's volume 550 metre cube.Find the area of the base.

Answer 1

Let the height be 7x meters

So, the radius be 5x meters

According to Question,

Volume of Cylinder = 550 m³

Πr²h = 550 m³

22 / 7 × (5x)² × 7x = 550

⇒ 22 / 7 × 25 × x² × 7 × x = 550

⇒ 22 × 25 × x³ = 550

⇒ 550 × x³ = 550

⇒ x³ = 550 / 550

⇒ x³ = 1

⇒ x = ∛1

⇒ x = 1

Required Measurements »

Radius = 5x = 5(1) = 5 m

Height = 7x = 7(1) = 7 m

Hence, the Radius and the Height of the Cylinder are 5 meters and 7 meters respectively.

∴ Area of the Base of Cylinder

= Area of Circle

= Πr²

= [ 22 / 7 × 5² ] m²

= [ 22 / 7 × 25 ] m²

= [ 550 / 7 ] m²

= 78 whole 4 / 7 m²

≈ 78.57 m²

Hence, the area of the Base of the Cylinder is [550 / 7] m²

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Answer 2

Let height and radius of cylinder be in ratio of 7x:5x

Given, volume of cylinder = 550 m³

Volume of cylinder = πr²h

550 = (22/7)×(5x)²×(7x)

550/22=25x³

x³ = 1

x= 1

So , height of cylinder = 7x = 7 m

and radius of cylinder = 5x = 5 m.