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
11.5
8.8
14.3
2.5
To find the slant height of the cone, we can use the Pythagorean theorem. The height of the cone (h) is given as 6 cm and the diameter (d) is given as 13 cm.
Using the Pythagorean theorem, the equation is:
r^2 + h^2 = s^2
where r is the radius, h is the height, and s is the slant height.
We can substitute the given values:
(13/2)^2 + 6^2 = s^2
(169/4) + 36 = s^2
(169 + 144) / 4 = s^2
313 / 4 = s^2
Now, we can solve for s by taking the square root of both sides:
sqrt(313 / 4) = sqrt(s^2)
sqrt(313) / sqrt(4) = s
17.7 / 2 = s
8.8 = s
Therefore, the slant height of the cone must be 8.8 cm, rounded to the nearest tenth. The correct answer is 8.8.