Question

The difference between the outside nad inside surface of a cylinder pype 14cm long is 44cm2 if the pipe is made of 99cm3 of metal find the outer and inner radii of the pipe

Answer 1

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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

⇒  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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