Answer:
V = 78776.32 mi³
see below for work
Step-by-step explanation:
You want the volume of a cone with base radius 28 mi, and slant height 100 mi.
Height
The formula for the volume of a cone requires we know the perpendicular distance from the base to the peak. That can be found using the Pythagorean theorem. For radius r and slant height s, the height h of the cone is found using ...
[tex]r^2+h^2=s^2\\\\h=\sqrt{s^2-r^2}\\\\h=\sqrt{100^2-28^2}=\sqrt{10000-784}=\sqrt{9216}\\\\h=96\quad\text{mi}[/tex]
Volume
The volume is found using the formula ...
[tex]V=\dfrac{\pi}{3}r^2h\\\\\\V=\dfrac{3.14}{3}(28\text{ mi})^2(96\text{ mi})=\dfrac{3.14\cdot784\cdot96}{3}\text{ mi}^3\\\\\\\boxed{V=78776.32\text{ mi}^3}[/tex]
