The volume of empty space in the Can is [tex]8.49 \ in^{3}[/tex].
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape or circle, and the center of the two bases are joined by a line segment, which is called the axis.
The given data are:
Diameter of the ball ([tex]d[/tex])[tex]=2.25 \ in[/tex]
The radius of the ball ([tex]r[/tex])[tex]=1.125 \ in[/tex]
Diameter of Can ([tex]D[/tex])[tex]=2.25 \ in[/tex]
The radius of Can ([tex]R[/tex])[tex]=2.25/2=1.125 \ in[/tex]
Height of can ([tex]H[/tex])[tex]=6.75 \ in[/tex]
[tex]\therefore[/tex]The volume of one ball[tex]=V_{1} =\frac{4}{3}\pi r^{3}[/tex]
[tex]V_{1}=\frac{4}{3}\ast 3.14\ast 1.125^{3} \\ V_{1}=5.96109 \ in^{3}[/tex]
The volume of 3 balls,
[tex]V_{2}=3\ast V_{1}=3\ast 5.96109=17.88327 \ in^{3}[/tex]
The volume of Can ([tex]V_3[/tex])[tex]=\pi \ast R^{2} \ast H[/tex]
[tex]V_3=\pi \ast1.125^2 \ast6.75\\V_3=26.8249[/tex]
The volume of empty space in Can([tex]V[/tex])[tex]=V_3-V_2[/tex]
[tex]V=26.8249-17.88327\\V=8.94163\approx 8.94[/tex]
Learn more about the topic Cylinder: https://brainly.com/question/26401820
