To find the slant height of the cone, we can use the Pythagorean theorem. The slant height, height, and radius of the cone form a right triangle.
The diameter of the cone is given as 13 cm. Therefore, the radius \( r \) is half of the diameter:
\[ r = \frac{d}{2} = \frac{13 , \text{cm}}{2} = 6.5 , \text{cm} \]
The height \( h \) of the cone is given as 6 cm.
Applying the Pythagorean theorem:
\[ l^2 = h^2 + r^2 \]
where \( l \) is the slant height. Substituting the known values:
\[ l^2 = 6^2 + 6.5^2 \]
Calculating \( 6^2 \) and \( 6.5^2 \):
\[ 6^2 = 36 \] \[ 6.5^2 = 42.25 \]
Adding these values:
\[ l^2 = 36 + 42.25 = 78.25 \]
Now, we find \( l \) by taking the square root:
\[ l = \sqrt{78.25} \approx 8.8 , \text{cm} \]
Thus, the slant height of the cone, rounded to the nearest tenth, is 8.8 cm.
The correct response is: 8.8 cm.