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)
• 11.5 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the slant height, we can use the Pythagorean theorem. The height of the cone is given as 6 cm, and the diameter is 13 cm.

The radius of the cone is half of the diameter, so it is 13/2 cm = 6.5 cm.
Now, we can use the Pythagorean theorem to find the slant height.
The slant height, height, and radius form a right triangle.
Using the theorem, we have:
(height)^2 + (radius)^2 = (slant height)^2
(6 cm)^2 + (6.5 cm)^2 = (slant height)^2
36 cm^2 + 42.25 cm^2 = (slant height)^2
78.25 cm^2 = (slant height)^2
Taking the square root of both sides, we have:
slant height = √(78.25 cm^2)
slant height ≈ 8.8 cm
Rounded to the nearest tenth, the slant height is 8.8 cm.

Therefore, the slant height must be approximately 8.8 cm.