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 point)
Responses

2.5 cm 

14.3 cm

11.5 cm

 8.8 cm

Answer 1

11.5 cm

Answer 2

how do I get that answer

Answer 3

To find the slant height of the cone, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

a^2 + b^2 = c^2

In this case, the height of the cone is given as 6 cm, and the radius (which is half the diameter) is 6.5 cm.

So, a = 6 cm (height)
b = 6.5 cm (radius)
c = slant height (what we want to find)

Plugging into the formula:
6^2 + 6.5^2 = c^2
36 + 42.25 = c^2
78.25 = c^2
c = √78.25
c ≈ 8.8 cm

Therefore, the slant height of the cone should be approximately 8.8 cm.