Question

The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm² and the volume of material in it is 1056 cm³. Find its internal and external radii. Given that the height of the cylinder is 21 cm.

Answer 1

Let R and r be the outer and inner radii of hollow metallic cylinder.

Let h be height of the metallic cylinder.

It is given that

Outer curved surface area + Inner curved surface area = 1056

`=>` 2πRh + 2πrh = 1056

`=>` 2πh(R + r) = 1056

`=> 2 xx 22/7 xx 21 (R + r) = 1056` 

`=> R + r = (1056 xx 7)/(2 xx 22 xx 21)`

`=>` R + r = 8   ...(i)

Volume of material in it = 1056 cm³ 

`=>` πR²h – πr²h = 1056

`=>` πh(R² – r²) = 1056

`=> 22/7 xx 21 (R^2 - r^2) = 1056`

`=> R^2 - r^2 = (1056 xx7)/(22xx21)`

`=>` (R + r)(R – r) = 16

`=>` 8 × (R – r) = 16

`=>` R – r = 2   ...(ii)

Adding (i) and (ii), we get

2R = 10 `=>` R = 5 cm

`=>` 5 – r = 2

`=>` r = 3 cm

∴ Internal radius = 3 cm and External radius = 5 cm