Answer:
The volume of the cone is 3,434 cubic km
Explanation:
The volume of a cone is calculated using the formula:
[tex]V=\frac{1}{3}\pi r^2h\text{ where }\begin{cases}r={Radius} \\ h={Perpendicular\;Height}\end{cases}[/tex]
From the given diagram, the diameter of the cone = 27 km.
[tex]Radius,r=\frac{Diameter}{2}=\frac{27}{2}=13.5\;km[/tex]
Next, we find the perpendicular height of the cone using the Pythagorean Theorem:
[tex]\begin{gathered} h^2+13.5^2=22.5^2 \\ h^2=22.5^2-13.5^2 \\ h=\sqrt{22.5^2-13.5^2} \\ h=18\text{ km} \end{gathered}[/tex]
Substitute r=13.5, h=18, and π=3.14 into the formula:
[tex]\begin{gathered} V=\frac{1}{3}\times3.14\times13.5^2\times18 \\ =3433.59 \\ \approx3434\;km^3 \end{gathered}[/tex]
The volume of the cone is 3,434 cubic km (to the nearest whole number).
