Given:
The diameter of the ball is 2.5inches.
So the radius is
[tex]r=1.25in[/tex]
The height of the cylinder is,
[tex]\begin{gathered} h=3\times2.5 \\ =7.5in \end{gathered}[/tex]
Required:
To find the Volume of the empty space.
Explanation:
Now the volume of the one ball is,
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ =\frac{4}{3}\pi(1.25)^3 \\ \\ =2.6041in^3 \end{gathered}[/tex]
Now the volume of the three ball is,
[tex]\begin{gathered} V=3\times2.6041 \\ =7.8125in^3 \end{gathered}[/tex]
The volume of the cylinder is,
[tex]\begin{gathered} V=\pi r^2h \\ =\pi\times1.25^2\times7.5 \\ =11.71875\pi in^3 \end{gathered}[/tex]
The volume of the empty space is = volume of the cylinder - volume of the balls.
[tex]\begin{gathered} =11.71875\pi-7.8125\pi \\ =3.91\pi in^3 \end{gathered}[/tex]
Final Answer:
Volume of the empty space is
[tex]3.91\pi in^3[/tex]
