Question

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)Responses2.5 cm2.5 cm11.5 cm11.5 cm14.3 cm14.3 cm8.8 cm8.8 cm

Answer 1

To find the slant height of the cones, we can use the Pythagorean Theorem.

The Pythagorean Theorem states:
\[
a^2 + b^2 = c^2
\]
where:
- \(a\) is one leg of the right triangle (height of the cone),
- \(b\) is the other leg of the right triangle (the radius of the base of the cone),
- \(c\) is the hypotenuse (the slant height of the cone).

Given:
- Height (\(a\)) = 6 cm
- Diameter = 13 cm, so the radius (\(b\)) = \( \frac{13}{2} = 6.5 \) cm

Now we can plug in the values into the Pythagorean Theorem:

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

Calculating \(6^2\) and \(6.5^2\):
\[
6^2 = 36
\]
\[
6.5^2 = 42.25
\]

Now add these two results:
\[
36 + 42.25 = c^2
\]
\[
78.25 = c^2
\]

Now take the square root to find \(c\):
\[
c = \sqrt{78.25} \approx 8.8 \text{ cm}
\]

Therefore, the slant height of the cone is approximately **8.8 cm**.