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) Responses 2.5 cm 2.5 cm 8.8 cm 8.8 cm 14.3 cm 14.3 cm 11.5 cm 11.5 cm

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, where:

• The height (h) of the cone is 6 cm.
• The radius (r) of the cone is half of the diameter. Given the diameter is 13 cm, the radius is \( r = \frac{13}{2} = 6.5 \) cm.
• The slant height (l) is the hypotenuse of the triangle.

According to the Pythagorean theorem:

\[ l^2 = h^2 + r^2 \]

Substituting in the values:

\[ l^2 = 6^2 + 6.5^2 \]

Calculating \( 6^2 \) and \( 6.5^2 \):

\[ 6^2 = 36 \] \[ 6.5^2 = 42.25 \]

Now, add these two values:

\[ l^2 = 36 + 42.25 = 78.25 \]

Next, take the square root to find \( l \):

\[ l = \sqrt{78.25} \approx 8.8 \]

Thus, the slant height of the cone is approximately 8.8 cm.