Question

I have been trying to figure this out and i cannot

Answer 1

The composite solid is a rectangular parallelepiped with a square base, with a hole in the middle in the shape of a cylinder. The volume of this solid is given by the difference between the volume of the parallelepiped and the volume of the cylinder. The volume of both figures is given by the area of the base, times the height of the solid.

$\begin{gathered} V_p=A_s\times h \\ V_c=A_c\times h \end{gathered}$

Then, we can factor out the height when calculating the difference between the volumes, this way we just have to calculate the difference between the area of the basis.

$V=V_p-V_c=A_s\times h-A_c\times h=(A_s-A_c)\times h$

The area of a square is given by the product between its side length and itself.

$A_s=s\times s=s^2$

The area of a circle is given by the following formula

$A_c=\frac{\pi d^2}{4}$

Where d represents the diameter. The square base of the parallelepiped has a length of 4 inches, and the diameter of the hole is 2 inches.

Using the area formulas on the formula for the volume, and the given values for the square side length and diameter, we have

$\begin{gathered} V=(A_s-A_c)\times h=(s^2-\frac{\pi d^2}{4})\times h \\ =((4)^2-\frac{\pi(2)^2}{4})\times16=(16-\frac{4\pi}{4})\times16 \\ =(16-3.14)\times16=12.86\times16 \\ =205.76 \end{gathered}$

The volume of this solid is 205.76 in.³.