To find the height of a cone given the radius and the slant height, you can use the Pythagorean theorem.
The formula is: \[ l^2 = r^2 + h^2 \] where:
- \( l \) is the slant height (13 cm)
- \( r \) is the radius (10 cm)
- \( h \) is the height we need to find
First, we identify the values:
- \( l = 13 \) cm
- \( r = 10 \) cm
Now, we can substitute these values into the formula: \[ 13^2 = 10^2 + h^2 \]
Calculating the squares: \[ 169 = 100 + h^2 \]
Next, subtract 100 from both sides: \[ 169 - 100 = h^2 \] \[ 69 = h^2 \]
Now, take the square root of both sides to find \( h \): \[ h = \sqrt{69} \]
Calculating \( \sqrt{69} \): \[ h \approx 8.31 \text{ cm} \]
So, the height of the cone is approximately 8.31 cm.