Question

I need help with #10 It says to also round to the nearest hundredth. Please help!

Answer 1

In general, one can obtain the volume of a sphere and a cube using the formulas below

`\begin{gathered} V_(cube)=l^3 \\ l\rightarrow\text{ side of the cube} \\ V_(sphere)=(4)/(3)\pi r^3 \\ r\rightarrow\text{ radius} \end{gathered}`

In our case, we need to subtract the volume of the hollow sphere from the volume of the cube, as shown below

`\begin{gathered} V_(cube)=18^3 \\ and \\ V_(sphere)=(4)/(3)\pi(9)^3 \\ \Rightarrow V_(foam)=V_(cube)-V_(sphere) \\ \Rightarrow V_(foam)=2778.371... \end{gathered}`

Rounding to the nearest hundredth,

`\Rightarrow V_(foam)\approx2778.37`

The answer is 2778.37in^3