Answer:
314 m³
Step-by-step explanation:
The volume (V) of a cone is calculated using the formula
V = [tex]\frac{1}{3}[/tex]πr²h
where r is the radius and h the perpendicular height
To find h use the right triangle from the vertex to the midpoint of the base and the radius.
Using Pythagoras' identity on the right triangle
where the slant height is the hypotenuse, then
h² + 5² = 13²
h² + 25 = 169 ( subtract 25 from both sides )
h² = 144 ( take the square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12, hence
V = [tex]\frac{1}{3}[/tex]π × 5² × 12
= π × 25 × 4 = 100π ≈ 314 m³
