we know that
The volume of the ball (sphere) is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
In this problem we have
[tex]V=4.19\ in^{3}[/tex]
Find the radius of the sphere
[tex]r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
Substitute the value of V
[tex]r=\sqrt[3]{\frac{3*4.19}{4\pi}}=1\ in[/tex]
for the calculation of the total volume I will assume that each ball is a cube
The volume of each ball is
[tex]V=b^{3}[/tex]
where
b is the diameter of the ball
[tex]b=1*2=2\ in[/tex]
Substitute
[tex]V=2^{3}=8\ in^{3}[/tex] ------> volume of each ball in the shape of cube
so
Multiply by [tex]64[/tex]
[tex]64*8=512\ in^{3}[/tex]
therefore
the answer is
[tex]512\ in^{3}[/tex]
