if you knew that the slant height of the cone = 13 cm and the radius of the cone = 5cm how would you find the height of the cone .
show the steps
To find the height of the cone, we can use the Pythagorean theorem.
Step 1: Start by using the Pythagorean theorem formula which states that a^2 + b^2 = c^2, where a and b are the two sides of a right triangle and c is the hypotenuse.
Step 2: In this case, the radius (r) of the cone is one of the legs of the right triangle, and the height (h) of the cone is the other leg. The slant height (l) is the hypotenuse.
Step 3: Substitute the given values into the formula: (5)^2 + h^2 = (13)^2
Step 4: Solve for h: 25 + h^2 = 169
h^2 = 169 - 25
h^2 = 144
h = √144
h = 12
Therefore, the height of the cone is 12 cm.