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

Answer 1

[AI-generated answer — Bot GPT 3.5]

Step 1: Use the Pythagorean theorem to find the height of the cone. The slant height, height, and radius form a right triangle. So we can use the formula:

\( height = \sqrt{slant\ height^2 - radius^2} \)

Step 2: Substitute in the given values:

\( height = \sqrt{13^2 - 5^2} \)

Step 3: Calculate the values inside the square root:

\( height = \sqrt{169 - 25} = \sqrt{144} \)

Step 4: Finally, find the square root of 144:

\( height = 12 \) cm

Therefore, the height of the cone is 12 cm.