Calculate the volume of a wedge cut from the base of a cylinder of radius a by a plane passing through a diameter of the base andinclined at an angle of 45 degrees to the base.

Introduction

The method of moving slices consists of slicing the figure, vertically or horizontally into slices. We apply it here to computing the volume of a circular wedge.

Cut the wedge

Method of moving slices

Equation of the base of the cylinder

Volume of the wedge

We get the volume of the wedge by filling it with a very large number of very thin slices, that is by integrating dV from x = 0 to x = a.