Question

The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 $m^2$.If the pipe is made of 99 $c{m}^3$ of metal,find the outer and inner radii of the pipe.

Answer 1

Solution:

Let r and R be the inner and outer radius of the cylindrical metallic pipe respectively.

h be the height of the metallic pipe = 14 cm

Difference between the Curved surface area of the outer cylinder and Curved surface area of the inner cylinder = 2πRh - 2πrh.

Given that difference between the outside and inside curved surface area of cylinder is 44 cm² .

⇒ 2πh( R - r) = 44

⇒ $\frac{44}{7}\times$ 14 ( R - r) = 44

⇒ R - r = $\frac{1}{2}$ = 0.5 ----------(1)

Given the pipe is made up of 99 cubic cm of metal so that

Volume of cylindrical metallic pipe = πR²h - πr²h.

⇒ $\frac{22}{7}\times$ 14 (R² - r²) = 99 cm³ .

⇒ $44\times$ (R² - r²) = 99

⇒ (R² - r²) =$\frac{9}{4}$ = 2.25

⇒ ( R - r)(R + r) = 2.25

= (0.5)$\times$(R + r) = 2.25

R + r = $\frac{2.25}{0.5}$ = 4.5

R + r = 4.5 ------------ (2)

Adding (1) and (2) we get

2R = 4.5 + 0.5 = 5

∴ R = 2.5 cm and r = 2 cm

∴ Outer side radius R = 2.5 cm and inner side radius r = 2 cm.