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

Answer 1

To find the slant height of the cone, we can use the Pythagorean Theorem. The theorem states that for a right triangle:

\( a^2 + b^2 = c^2 \)

Where:
- \( a \) is the height of the cone
- \( b \) is the radius of the base of the cone
- \( c \) is the slant height of the cone

Given:
- The height (\( a \)) of the cone is 6 cm.
- The diameter of the cone is 13 cm, so the radius (\( b \)) is half of that, which is \( \frac{13}{2} = 6.5 \) cm.

Now, we can plug these values into the Pythagorean theorem.

1. Square the height and the radius:
- \( a^2 = 6^2 = 36 \)
- \( b^2 = (6.5)^2 = 42.25 \)

2. Now apply the Pythagorean theorem:
- \( c^2 = a^2 + b^2 \)
- \( c^2 = 36 + 42.25 = 78.25 \)

3. Now solve for \( c \) (the slant height):
- \( c = \sqrt{78.25} \)
- \( c \approx 8.839 \)

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

So the answer is **8.8 cm**.