Question

Please help me with this!!!

Answer 1

Answer:

314 m³

Step-by-step explanation:

The volume (V) of a cone is calculated using the formula

V = $\frac{1}{3}$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 = $\sqrt{144}$ = 12, hence

V = $\frac{1}{3}$π × 5² × 12

   = π × 25 × 4 = 100π ≈ 314 m³