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 nearest tenth

a. 11.5 cm
b. 8.8 cm
c. 2.5 cm
d. 14.3 cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

So, in this case, the height of the cone is 6 cm and the radius (half the diameter) is 6.5 cm. Applying the Pythagorean Theorem:

hypotenuse^2 = height^2 + radius^2
hypotenuse^2 = 6^2 + 6.5^2
hypotenuse^2 = 36 + 42.25
hypotenuse^2 = 78.25
hypotenuse ≈ √78.25
hypotenuse ≈ 8.8

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

b. 8.8 cm.