Question

The difference between the outer curved surface area and the inner curved surface area of a hollow cylinder is 352 cm². If its height is 28 cm and the volume of material in it is 704 cm³; find its external curved surface area.

Answer 1

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

Let h be the height of the metallic cylinder.

It is given that

Outer curved surface area - Inner curved surface area = 352

`=>` 2πRh – 2πrh = 352

`=>` 2πh(R – r) = 352

`=> 2xx22/7xx28 (R - r) = 352`

`=> R - r = (352 xx 7)/(2xx22xx28)`

`=>` R – r = 2   ...(i) 

Volume of material in it = 704 cm³ 

`=>` πR²h – πr²h = 704

`=>` πh(R² – r²) = 704

`=> 22/7 xx 28(R^2 - r^2) = 704`

`=> R^2 - r^2 = (704 xx 7)/(22xx28)`

`=>` (R + r)(R – r) = 8

`=>` (R + r) × 2 = 8

`=>` R + r = 4    ...(ii)

Adding (i) and (ii) we get

2R = 6

`=>` R = 3 cm

∴ External curved surface area = 2πRh

= `2 xx 22/7 xx 3 xx 28`

= 2 × 22 × 3 × 4

= 528 cm²