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?
and what would be the steps
and what would be the steps
Answers
GPT 3.5
To find the height of the cone, you can use the Pythagorean theorem.
Step 1: Identify the slant height (l), radius (r), and height (h) of the cone.
Given: l = 13 cm, r = 5 cm
Step 2: Use the Pythagorean theorem to set up an equation relating the slant height, radius, and height of the cone.
l^2 = r^2 + h^2
Step 3: Substitute the given values to the equation.
(13)^2 = (5)^2 + h^2
169 = 25 + h^2
144 = h^2
Step 4: Solve for h by taking the square root of both sides.
sqrt(144) = sqrt(h^2)
12 = h
Therefore, the height of the cone is 12 cm.
Step 1: Identify the slant height (l), radius (r), and height (h) of the cone.
Given: l = 13 cm, r = 5 cm
Step 2: Use the Pythagorean theorem to set up an equation relating the slant height, radius, and height of the cone.
l^2 = r^2 + h^2
Step 3: Substitute the given values to the equation.
(13)^2 = (5)^2 + h^2
169 = 25 + h^2
144 = h^2
Step 4: Solve for h by taking the square root of both sides.
sqrt(144) = sqrt(h^2)
12 = h
Therefore, the height of the cone is 12 cm.