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?
Step 1
Step 2
Step 3
Step 4
Step 1
Step 2
Step 3
Step 4
Answers
GPT 3.5
Step 1: Use the Pythagorean theorem to find the height of the cone.
Step 2: The slant height of the cone is the hypotenuse, the radius is one of the legs, and the height of the cone is the other leg. So, we have a right triangle with sides of 5 cm (radius), h cm (height), and 13 cm (slant height).
Step 3: Using the Pythagorean theorem, we have:
\[ 5^2 + h^2 = 13^2 \]
\[ 25 + h^2 = 169 \]
\[ h^2 = 169 - 25 \]
\[ h^2 = 144 \]
\[ h = \sqrt{144} \]
\[ h = 12 \text{ cm} \]
Step 4: Therefore, the height of the cone is 12 cm.
Step 2: The slant height of the cone is the hypotenuse, the radius is one of the legs, and the height of the cone is the other leg. So, we have a right triangle with sides of 5 cm (radius), h cm (height), and 13 cm (slant height).
Step 3: Using the Pythagorean theorem, we have:
\[ 5^2 + h^2 = 13^2 \]
\[ 25 + h^2 = 169 \]
\[ h^2 = 169 - 25 \]
\[ h^2 = 144 \]
\[ h = \sqrt{144} \]
\[ h = 12 \text{ cm} \]
Step 4: Therefore, the height of the cone is 12 cm.