Answer:
[tex]V=122.5in^3[/tex]
Step-by-step explanation:
The volume of a right circular cone is given by:
[tex]V=\frac{\pi r^2h}{3}[/tex]
where r is the radius of the circle and h is the height of the cone, and [tex]\pi[/tex] is a constant [tex]\pi=3.1416[/tex].
According to the problem the height is:
[tex]h=8.1 in[/tex]
and we don't have the radius but we have the diameter, which is useful to find it. We just divide the diameter by 2 to find the radius:
[tex]r=\frac{d}{2}=\frac{7.6in}{3}=3.8in[/tex]
Now, we can find the volume by substituting all the known values:
[tex]V=\frac{\pi r^2h}{3}[/tex]
[tex]V=\frac{(3.1416)(3.8in)^2(8.1in)}{3} \\\\V=\frac{(3.1416)(14.44in^2)(8.1in)}{3} \\\\V=\frac{367.454in^3}{3} \\\\V=122.485[/tex]
Rounding the volume to the nearest tenth of cubic inch we get:
[tex]V=122.5in^3[/tex]
