Question

Find the volume of the box with the bowl shaped head out of the top. What is the volume of the rectangular prism only?

Answer 1

The Solution:

Given:

We are required to find the volume of the box only.

By formula, the volume of the box is:

`\begin{gathered} V=L* B* H \\ In\text{ this case,} \\ V=volume=? \\ L=length=10cm \\ B=10cm \\ H=13cm \end{gathered}`

Substitute these values in the formula.

`V=10*10*13=1300cm^3`

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:

`r=(diameter)/(2)=\frac{length\text{ of the box}}{2}=(10)/(2)=5cm`

The volume of a hemisphere is:

`V=(2\pi r^3)/(3)=(2\pi*5^3)/(3)=261.7994cm^3`

The volume of the box with the bowl-shaped head out is:

`V=(10*10*13)-(2\pi(5^3))/(3)=1300-261.7994=1038.201\approx1038.2cm^3`

Thus, the correct answer is 1038.2 cubic centimeters.