Volume of a Cone Math Example 4

Solution

1. 1
   Step 1: Use the Pythagorean theorem to find the vertical height. In a right triangle formed by the radius, height, and slant height: $h^2 + r^2 = l^2$, so $h^2 + 5^2 = 13^2$, giving $h^2 = 169 - 25 = 144$, thus $h = 12$ cm.
2. 2
   Step 2: Now compute the volume: $V = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (5)^2 (12) = \frac{1}{3}\pi \times 300 = 100\pi$ cm³.