Answer:
[tex]V=\pi^{}mi^3[/tex]
Explanation:
Step 1. Let h be the height of the cone:
[tex]h=3mi[/tex]
and let d be the diameter of the circle:
[tex]d=2mi[/tex]
From the diameter we can find the radius of the circle:
[tex]\begin{gathered} r=\frac{d}{2} \\ \downarrow\downarrow \\ r=\frac{2mi}{2} \\ \downarrow\downarrow \\ r=1mi \end{gathered}[/tex]
Step 2. To find the volume of a cone we use the following formula:
[tex]V=\frac{\pi r^2h}{3}[/tex]
Step 3. Substituting the values of r and h into the formula:
[tex]V=\frac{\pi(1mi)^2(3mi)}{3}[/tex]
Solving the operations:
[tex]\begin{gathered} V=\frac{\pi(1mi^2)(3mi)}{3} \\ \downarrow\downarrow \\ V=\frac{3\pi^{}}{3}mi^3 \end{gathered}[/tex]
The result is:
[tex]V=\pi^{}mi^3[/tex]
The volume is pi cubic miles.
Answer:
[tex]V=\pi^{}mi^3[/tex]
