The Solution:
Given:
We are required to find the volume of the box only.
By formula, the volume of the box is:
[tex]\begin{gathered} V=L\times B\times H \\ In\text{ this case,} \\ V=volume=? \\ L=length=10cm \\ B=10cm \\ H=13cm \end{gathered}[/tex]
Substitute these values in the formula.
[tex]V=10\times10\times13=1300cm^3[/tex]
Thus, the volume of the rectangular prism only is 1300 cubic centimeters
The second part of the question is to find the volume of the box with the bowl-shaped head out.
The radius of the hemisphere is:
[tex]r=\frac{diameter}{2}=\frac{length\text{ of the box}}{2}=\frac{10}{2}=5cm[/tex]
The volume of a hemisphere is:
[tex]V=\frac{2\pi r^3}{3}=\frac{2\pi\times5^3}{3}=261.7994cm^3[/tex]
The volume of the box with the bowl-shaped head out is:
[tex]V=(10\times10\times13)-\frac{2\pi(5^3)}{3}=1300-261.7994=1038.201\approx1038.2cm^3[/tex]
Thus, the correct answer is 1038.2 cubic centimeters.
