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

${\displaystyle \Rightarrow }$ 2πRh – 2πrh = 352

${\displaystyle \Rightarrow }$ 2πh(R – r) = 352

${\displaystyle \Rightarrow 2\times \frac{22}{7}\times 28(R-r)=352}$

${\displaystyle \Rightarrow R-r=\frac{352\times 7}{2\times 22\times 28}}$

${\displaystyle \Rightarrow }$ R – r = 2   ...(i) 

Volume of material in it = 704 cm³ 

${\displaystyle \Rightarrow }$ πR²h – πr²h = 704

${\displaystyle \Rightarrow }$ πh(R² – r²) = 704

${\displaystyle \Rightarrow \frac{22}{7}\times 28(R^2-r^2)=704}$

${\displaystyle \Rightarrow R^2-r^2=\frac{704\times 7}{22\times 28}}$

${\displaystyle \Rightarrow }$ (R + r)(R – r) = 8

${\displaystyle \Rightarrow }$ (R + r) × 2 = 8

${\displaystyle \Rightarrow }$ R + r = 4    ...(ii)

Adding (i) and (ii) we get

2R = 6

${\displaystyle \Rightarrow }$ R = 3 cm

∴ External curved surface area = 2πRh

= ${\displaystyle 2\times \frac{22}{7}\times 3\times 28}$

= 2 × 22 × 3 × 4

= 528 cm²