Given:
The dimension of the spherical ball is a diameter of 4in. That is the radius,
[tex]r=2in[/tex]
The dimensions of the cylinder are,
[tex]\begin{gathered} Radius,r=2in \\ Height,h=4in \end{gathered}[/tex]
The dimensions of the rectangular are
[tex]\begin{gathered} Length,l=4in \\ Breadth,b=4in \\ Height,h=4in \end{gathered}[/tex]
To find:
The option which has less waste place.
Explanation:
The volume of the sphere is,
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ =\frac{4}{3}\times\frac{22}{7}\times2^3 \\ =33.52in^3 \end{gathered}[/tex]
The volume of the cylinder is,
[tex]\begin{gathered} V=\pi r^2h \\ =\frac{22}{7}\times2^2\times4 \\ =50.29in^3 \end{gathered}[/tex]
The volume of the rectangle is,
[tex]\begin{gathered} V=lbh \\ =4\times4\times4 \\ =64in^3 \end{gathered}[/tex]
After fitting the spherical ball in the cylinder box, the remaining waste place will be,
[tex]50.29-33.52=16.77in^3...........(1)[/tex]
After fitting the spherical ball in the rectangular box, the remaining waste place will be,
[tex]64-33.52=30.48in^3.........(2)[/tex]
Comparing (1) and (2), we get to know that the cylinder will have less waste place.
Final answer:
Option 1 - cylinder
