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.

Question

1. 8.8 cm
2. 2.5 cm
3. 14.3 cm
4. 11.5 cm

Answer 1

To find the slant height of the cone, we can use the Pythagorean theorem. The slant height (l), the height (h), and the radius (r) form a right triangle.

1. First, we need to find the radius from the diameter. The diameter is 13 cm, so the radius \( r \) is: \[ r = \frac{\text{diameter}}{2} = \frac{13 \text{ cm}}{2} = 6.5 \text{ cm} \]

2. Now, we have:

   • Height \( h = 6 \) cm
   • Radius \( r = 6.5 \) cm

3. We can apply the Pythagorean theorem, which states that: \[ l^2 = h^2 + r^2 \]

4. Substituting the values: \[ l^2 = 6^2 + 6.5^2 \] \[ l^2 = 36 + 42.25 \] \[ l^2 = 78.25 \]

5. Next, we take the square root of both sides to find \( l \): \[ l = \sqrt{78.25} \approx 8.8 \text{ cm} \]

Thus, the slant height is approximately 8.8 cm.

The answer is 1. 8.8 cm.