Part A.
To determine the volume of the barrel we use the formula for the volume of a cylinder:
[tex]V=r^2\pi h,[/tex]
where r is the radius of the base of the cylinder and h is its height.
For the barrel:
[tex]\begin{gathered} h=27\text{ in, } \\ r=\frac{25\text{ in}}{2}=12.5in. \end{gathered}[/tex]
Substituting the above values in the formula, we get:
[tex]V=13246.875in^3.[/tex]
Answer part A:
[tex]V=13,246.875\imaginaryI n^3[/tex]
Part B.
Recall that:
[tex]1\text{ gallon=231in}^3.[/tex]
Answer part B: There are 231 cubic inches in 1 gallon.
Part C.
Diagram:
The barrel can contain 57 gallons of water, if it is at 2/3 of its capacity then there are
[tex]57gallons*\frac{2}{3}=38\text{ gallons}[/tex]
of water inside the barrel.
Answer part C:
[tex]38\text{ gallons.}[/tex]
