Q12 of 79 Page 244

A hollow cylindrical pipe is of length 40 cm. Its internal and external radii are 4 cm and 12 cm respectively. It is melted and cast into a solid cylinder of length 20 cm. Find the radius of the new solid.

Given, Length of cylindrical pipe (h) = 40 cm


Internal radius of the pipe (r) = 4 cm


External radius of the pipe (R) = 12 cm


Height of cylinder = 20 cm


Volume of hollow cylindrical pipe = Volume of cylinder


⇒ h (R2 - r2) = r2 h


⇒ h (R2 - r2) = r2 h


⇒ (40) (122 - 42) = r2 (20)


⇒ (40) (144 - 16) = r2 (20)


⇒ (40) = r2


⇒ r2 = (40)


⇒ r2 = 2 128


⇒ r2 = 256


⇒ r =


⇒ r = 16 cm


Therefore radius of cylinder = 16 cm


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