Question

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

Answer 1

HEY MATE...

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.

HOPE THIS HELP YOU...