Question

A solid sphere has a cylindrical portion cut out of theinside. The center of the cylinder is the center of thesphere. If the sphere has a radius of 10 and thecylinder has a radius of 4, what is the volume of thefigure if the cylinders height is ¾ the diameter of thesphere? Use 3.14 to approximate pi.

Answer 1

The volume of the figure will be the volume of the sphere minus the volume of the cylinder. The volume of the sphere will be:

`\begin{gathered} Vs=(4)/(3)\pi r^3 \\ where \\ r=10units \\ Vs\approx4186.67units^3 \end{gathered}`

The volume of the cylinder is:

`\begin{gathered} Vc=\pi r^2h \\ where\colon \\ r=4units \\ h=(3)/(4)(2\cdot10)=15units \\ so\colon \\ Vc=\pi(4^2)(15) \\ Vc\approx753.6units^3 \end{gathered}`

Therefore, the volume of the figure is:

`\begin{gathered} V=Vs-Vc \\ V=4186.67-753.6 \\ V=3433.07units^3 \end{gathered}`

Answer:

V = 3433.07 units³