Question

the difference between outside ainside surface of a cylindrical metallic pipe 14 cm long is 44 cm into square if the pipe is made of 99 cubic metres of metal find the outer and inner radii of the pipe

Answer 1

Sol:

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 cmDifference 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
⇒  44 / 7 x 14 ( R - r) = 44
⇒ R - r = 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.

⇒ 22/7 x 14 (R2 - r2) = 99 cm3 .
⇒ 44 x (R2 - r2) = 99
⇒ (R2 - r2) = 9 / 4 = 2.25
⇒ ( R - r)(R + r)  = 2.25
= (0.5)x(R + r) = 2.25
R + r = 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

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