A hole of diameter a is bored through the centre of a sphere of radius a. Show that the remaining volume is root3/2.pi.a(cubed).
A hole of diameter is bored through the centre of a sphere of radius
Show that the remaining volume is:Code:| * * * *:::::|:::::* - * - - - + - - - * - y = a/2 *| | |* | | | * | | | * ----*-+-------+-------+-*---- * | | | *a | | | *| | |* * - - - | - - - * * | * * * * |
The equation of the circle is: .
The equation of the horizontal line is: .
Revolve the shaded region about the -axis.
That is the desired volume.
The graphs intersect for: .
. . Substitute  into : .
Due to symmetry: . .