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

UpStudy AI · Accepted Answer

To find the slant height of the cone, we can use the Pythagorean Theorem. The slant height $$ l $$, height $$ h $$, and radius $$ r $$ of the cone form a right triangle, where:

$$
l = \sqrt{r^2 + h^2}
$$

Given:
- Height $$ h = 6 $$ cm
- Diameter $$ d = 13 $$ cm, so the radius $$ r = \frac{d}{2} = 6.5 $$ cm

Now, plug the values into the formula:

$$
l = \sqrt{(6.5)^2 + (6)^2} = \sqrt{42.25 + 36} = \sqrt{78.25} = 8.85 \text{ cm}
$$

Rounding to the nearest tenth:

$$
l \approx 8.9 \text{ cm}
$$

**Answer:** The slant height must be approximately 8.9 cm.
The slant height must be approximately 8.9 cm.

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