Question

A hollow cylindrical pipe, 100 m long is an elliptic cylinder, whose major radius is 50 mm and minor radius is 20 mm. Compute the volume of the pipe if the hole has a radius of 30 mm.

 

V= ______ cubic meters

Answer 1

Volume of the elliptical cylinder is 0.02×0.05×100π=0.10π cubic metres. The volume of a cylindrical hole 100m long is 100×0.03²π=0.09π cubic metres. The hole is drilled into the pipe. Therefore the volume of the pipe is the difference between the two volumes: 0.01π=0.03142 cubic metres approximately. However, the hole has a greater radius than the pipe (bigger than its minor radius), so should the size of the hole be 30mm in diameter? If so, the volume of the hole would be 0.0225π cubic meters and the volume of the solid part of the pipe would be 0.0775π=0.2435 cubic metres approximately.