Question

The internal surface area of a cylinder is equal to 616 centimetre square and radius is equal to half of his height then find the volume of Cylinder

Answer 1

Given :-

internal surface area of the cylinder = 616cm²

ATQ, the radius of the cylinder is half of the height of the cylinder.

let the radius of the cylinder be x

therefore it's height = 2x

we know that,

2πrh = lateral surface area of a cylinder

➡ 2πrh = 616cm²

➡ 2 × 22/7 × x × 2x = 616cm²

➡ 44/7 × 2x² = 616cm²

➡ 2x² = 616 × 7/44

➡ 2x² = 14 × 7

➡ x² = 98/2

➡ x = √49

➡ x = 7cm

hence,

• radius of the cylinder = x = 7cm

• height of the cylinder = 2x = 14cm

VERIFICATION :-

= 2 × 22/7 × 7 × 14

= 44 × 14

= 616cm²

hence verified!

now, volume of the cylinder = πr²h

= 22/7 × 7 × 7 × 14

= 22 × 7 × 14

= 2156cm³