Question

If you knew that the slant height of the cone = 13 cm, and the radius of the cone = 5 cm, how would you find the height of the cone?



(4 points)
Step 1
Step 2
Step 3
Step 4
Skip to navigation

Answer 1

Step 1: Draw a cross-section through the cone's axis. This gives a right triangle with hypotenuse = slant height (13 cm), one leg = radius (5 cm), and the other leg = height h.

Step 2: Use the Pythagorean theorem: l^2 = r^2 + h^2.

Step 3: Substitute values: 13^2 = 5^2 + h^2 → 169 = 25 + h^2 → h^2 = 144.

Step 4: Take the square root: h = √144 = 12 cm.

So the cone's height is 12 cm.