To find the slant height of the cone, we can use the Pythagorean Theorem. The relationship among the height (h), radius (r), and slant height (l) of the cone can be expressed as:
\[ l^2 = r^2 + h^2 \]
First, we need to determine the radius of the cone from the given diameter.
- The diameter \( d \) is given as 13 cm, so the radius \( r \) is: \[ r = \frac{d}{2} = \frac{13 , \text{cm}}{2} = 6.5 , \text{cm} \]
We are also given the height \( h \) of the cone as 6 cm.
Now we can substitute these values into the Pythagorean Theorem:
\[ l^2 = r^2 + h^2 \] \[ l^2 = (6.5 , \text{cm})^2 + (6 , \text{cm})^2 \] \[ l^2 = 42.25 , \text{cm}^2 + 36 , \text{cm}^2 \] \[ l^2 = 78.25 , \text{cm}^2 \]
Now, taking the square root to find \( l \):
\[ l = \sqrt{78.25} \] \[ l \approx 8.84 , \text{cm} \]
Rounding to the nearest tenth, we get:
8.8 cm.
So the correct response is 8.8 cm.