Question

A hollow copper pipe of inner radius 3 cm and outer radius 4cm is melted and changed into a solid right circular cylinder of the same !engh as that of the pipe. Find the area of the cross section of the solid cylinder.

Answer 1

Volume of the cylinder is given by πr^2h, where h is the height of the cylinder, r is the radius of the cylinder. radius of the inner cylinder is = 3cm radius of the outer cylinder is = 4cm Hence the volume of the hollow cylinder = volume of outer cylinder - volume of inner cylinder So volume of the hollow cylinder = π *(4)^2* h - π*(3)^2*h = 7πh And this volume is used to recaste a solid cylinder of same height, and let the radius be ŕ Hence volume of hollow cylinder = volume of solid cylinder So 7πh = πhŕ^2 Hence 7π = πŕ^2 So πŕ^2 is the area of cross section So area of cross section = 7π