Chem Tech makes paper cones used to filter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape, where the slant height is needed. The company wants the height of the cones to be 6 cm. If they make the diameter 13 cm, what must the slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth. (1 point) 14.3 cm 2.5 cm 8.8 cm 11.5 cm

To find the slant height of the cone using the Pythagorean Theorem, we first need to determine the radius and the height of the cone.

1. Diameter of the cone: 13 cm
   Radius \( r \):
   \[ r = \frac{diameter}{2} = \frac{13}{2} = 6.5 \text{ cm} \]

2. Height of the cone: 6 cm

3. Slant height \( l \): This is the hypotenuse of a right triangle where one leg is the radius and the other leg is the height. We can use the Pythagorean Theorem:
   \[ l^2 = r^2 + h^2 \] Substituting \( r = 6.5 \text{ cm} \) and \( h = 6 \text{ cm} \): \[ l^2 = (6.5)^2 + (6)^2 \] \[ l^2 = 42.25 + 36 \] \[ l^2 = 78.25 \]

4. Finding the slant height \( l \): \[ l = \sqrt{78.25} \approx 8.85 \text{ cm} \]

Rounded to the nearest tenth, the slant height is approximately 8.8 cm.

Thus, the answer is 8.8 cm.