The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m2. If the pipe is made of 99 cm3 of metal, find the outer and inner radii of the pipe.

Let the inner radius of pipe = r’


And the radius of outer cylinder = r’’


Length of cylinder (h) = 14 cm


Surface area of hollow cylinder =2πh (r’ –r’’)


Given surface area of cylinder = 44 m2.


2π h(r’’ – r’) = 44


2π (14) (r’’ – r’) = 44


(r2 – r1) =


(r2 – r1) = 1/2 ……. (1)


Given volume of a hollow cylinder = 99 cm3


Volume of a hollow cylinder = π h()


π h (r’’2 - r’2) = 99


14π (r''2 - r'2) = 99


14π (r’ + r’’) (r’’ – r’) = 99


14π (r’ +r’’) = 99


(r’ +r’’) = ……………… (2)


Equating (1) & (2) equations we get


r’’ = 5/2 cm


Substituting r2 value in (1)


r’ = 2 cm


Inner radius of pipe (r’) = 2 cm


Radius of outer cylinder (r’’) = 5/2 cm


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