The volume of a cone with radius r and height h, is:
[tex]V=\frac{1}{3}\pi r^2h[/tex]The diameter of the base of the cone has a lenght of 5 in. Since the radius of a circle is half its diameter, then the radius of the base of the cone is 2.5 in.
Substitute r=2.5 in and h=8in to find the volume of the cone:
[tex]\begin{gathered} V=\frac{1}{3}\pi(2.5in)^2\cdot(8in) \\ =\frac{50\pi}{3}in^3 \end{gathered}[/tex]In terms of π, the volume of the cone is:
[tex]\frac{50\pi}{3}in^3[/tex]Using a calculator to find a decimal expression, the volume of the cone is:
[tex]52.35987756\ldots in^3[/tex]