A drawing shows a circle showing diameter below a sector of a circle showing slant height. A double-headed arrow crossing the center of the circle is labeled as d equals diameter. A dotted double-headed arrow is drawn from the top point of the sector of the circle to a point along the curved edge. The arrow is labeled as lower L equals slant height.

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 the nearest tenth.

(1 point)
Responses

14.3 cm
14.3 cm

 8.8 cm
 8.8 cm

11.5 c

Answer 1

To find the slant height of the cone, we can use the Pythagorean Theorem. The relationship among the height (h), radius (r), and slant height (l) of the cone can be expressed as:

$$l^2=r^2+h^2$$

First, we need to determine the radius of the cone from the given diameter.

• The diameter $d$ is given as 13 cm, so the radius $r$ is: $$r=\frac{d}{2}=\frac{13,\text{cm}}{2}=6.5,\text{cm}$$

We are also given the height $h$ of the cone as 6 cm.

Now we can substitute these values into the Pythagorean Theorem:

$$l^2=r^2+h^2$$ $$l^2=(6.5,\text{cm}{)}^2+(6,\text{cm}{)}^2$$ $$l^2=42.25,{\text{cm}}^2+36,{\text{cm}}^2$$ $$l^2=78.25,{\text{cm}}^2$$

Now, taking the square root to find $l$:

$$l=\sqrt{78.25}$$ $$l\approx 8.84,\text{cm}$$

Rounding to the nearest tenth, we get:

8.8 cm.

So the correct response is 8.8 cm.