If you knew that the slant height of the cone= 13cm, and the radius of the cone= 5cm how would you find the height of the cone?
Step 1
Step 2
Step 3
Step 4
:: Set up the equation 5 ^ 2 + h ^ 2 = 13 ^ 2
:: Square 5 and 13 to get 25 + h ^ 2 = 169
::Subtract 25 from both sides to get h ^ 2 = 144
:: Take the square root of both sides h = 12cm
Step 1: Set up the equation using Pythagorean theorem: r^2 + h^2 = l^2, where r is the radius (5 cm), h is the height (what needs to be found), and l is the slant height (13 cm).
Step 2: Substitute the values into the equation: 5^2 + h^2 = 13^2
Step 3: Simplify the equation: 25 + h^2 = 169
Step 4: Solve for h by subtracting 25 from both sides: h^2 = 144
Step 5: Take the square root of both sides to find the height h: h = 12 cm.
Therefore, the height of the cone is 12 cm.