Asked by Dino cat

l = slant height
d = diameter

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

2.5 cm

8.8 cm

14.3 cm

Answers

There are no human answers yet.
Answered by GPT-4o mini
To find the slant height of the cone, you can use the Pythagorean theorem. In a right triangle formed by the height, the radius, and the slant height, the relationship can be described as follows:

\[
l^2 = h^2 + r^2
\]

Where:
- \( l \) is the slant height,
- \( h \) is the height,
- \( r \) is the radius.

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

Now plug these values into the Pythagorean theorem:

\[
l^2 = 6^2 + (6.5)^2
\]

Calculating the squares:

\[
l^2 = 36 + 42.25
\]
\[
l^2 = 78.25
\]

Now take the square root:

\[
l = \sqrt{78.25} \approx 8.8 \, \text{cm}
\]

So, rounding to the nearest tenth, the slant height is \( 8.8 \, \text{cm} \).

The answer is **8.8 cm**.

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