To find the height of the cone using the slant height and the radius, you can follow these steps:
Step 1: Set up the equation \(5^2 + h^2 = 13^2\)
Step 2: Square 5 and 13 to get \(25 + h^2 = 169\)
Step 3: Subtract 25 from both sides to get \(h^2 = 144\)
Step 4: Take the square root of both sides \(h = 12 , \text{cm}\)
This gives you the height of the cone as 12 cm.