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Asked by Shivam Meena

Nov 22, 2014

A cylindrical metallic pipe is 14cm long.The difference between the outside and inside surfaces is 44cm square.If the pipe is made up of 99 cubic cm of metal.Find the outer and inner radii of the pipe.

Raghunath Reddy

Member since Apr 11, 2014

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 cm

Difference between the Curved surface area of the outer cylinder and Curved surface area of the inner cylinder = 2Ï€Rh - 2Ï€rh.

Given that difference between the outside and inside curved surface area of cylinder is 44 cm^{2} .

â‡’ 2Ï€h( R - r) = 44

â‡’ 44 / 7 x 14 ( R - r) = 44

â‡’ 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 = Ï€R^{2}h - Ï€r^{2}h.

â‡’ 22/7 x 14 (R^{2} - r^{2}) = 99 cm^{3} .

â‡’ 44 x (R^{2} - r^{2}) = 99

â‡’ (R^{2} - r^{2}) = 9 / 4 = 2.25

â‡’ ( 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

âˆ´ R = 2.5 cm and r = 2 cm

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