Answer:
The exact value of the volume is equal to
[tex]V=19\frac{397}{512}\pi\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]D=5\frac{5}{8}\ in[/tex]
convert to an improper fraction
[tex]D=5\frac{5}{8}\ in=\frac{5*8+5}{8}=\frac{45}{8}\ in[/tex]
[tex]r=(45/8)/2=\frac{45}{16}\ in[/tex]
[tex]h=7\frac{1}{2}\ in=\frac{7*2+1}{2}=\frac{15}{2}\ in[/tex]
substitute in the formula of volume
[tex]V=\frac{1}{3}\pi (\frac{45}{16}^{2})(\frac{15}{2})=\frac{30,375}{1,536}\pi\ in^{3}[/tex]
Simplify
[tex]\frac{30,375}{1,536}=\frac{29,184}{1,536}+\frac{1,191}{1,536}=19\frac{397}{512}[/tex]
substitute
[tex]V=19\frac{397}{512}\pi\ in^{3}[/tex]
