Answer:
1.1783
Step-by-step explanation:
The attached picture shows a cross section of the cylindrical shell that it is convenient to use as a differential of the volume. The radius from the center of revolution is (1-x), so the circumference of the shell is 2π(1-x). Of course, its height is tan(x), so the differential of volume is ...
dV = 2π(1-x)tan(x)
The indefinite integral does not have a nice closed-form solution, but it can be easily integrated numerically from x = 0 to 1 by most scientific and graphing calculators. The attached shows the volume to be about 1.1783 cubic units.
