# How do you find the volume of the central part of the unit sphere that is bounded by the planes #x=+-1/5, y=+-1/5 and z=+-1/5#?

##### 2 Answers

#### Explanation:

The volume of the slice between

= twice the volume of the solid of revolution, about x-axis, of the

area enclosed by the circle

#= (148 pi )/375 cubic units.

The three slices for

have this volume and each includes, as intersection, the central

cube bounded by these planes.

So, the required volume

In making this solid, eight identical wedges, with spherical tops,

have been removed, one from each octant. The volume of each

= (volume of the unit sphere - volume of the solid made)