Question

the pythagorean theorem in three dimensions
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
○ 14.3 cm
○ 2.5 cm
○ 8.8 cm

Explanation:

Step1: Calculate radius of cone

The radius $r$ is half the diameter.
$r = \frac{13}{2} = 6.5$ cm

Step2: Apply 3D Pythagorean theorem

Slant height $l$ is hypotenuse of right triangle with legs $r$ and height $h=6$ cm.
$l = \sqrt{r^2 + h^2} = \sqrt{6.5^2 + 6^2}$

Step3: Compute and round result

Calculate the value and round to nearest tenth.
$l = \sqrt{42.25 + 36} = \sqrt{78.25} \approx 8.8$ cm

Answer:

8.8 cm (corresponding to the option: ○ 8.8 cm)