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 

14.3 cm
14.3 cm

 8.8 cm
 8.8 cm

11.5 cm
11.5 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the slant height, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.

In this case, one of the other sides is the height of the cone, which is given as 6 cm. The other side is half of the diameter, which is 13 cm/2 = 6.5 cm.

Using the Pythagorean Theorem, we have:

(slant height)^2 = (height)^2 + (radius)^2
(slant height)^2 = 6^2 + 6.5^2
(slant height)^2 = 36 + 42.25
(slant height)^2 = 78.25

Taking the square root of both sides, we find:

slant height = √78.25 ≈ 8.8 cm

Therefore, the slant height should be approximately 8.8 cm, so the correct answer is:

 8.8 cm