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

(1 point)
Responses

 8.8 cm
 8.8 cm

14.3 cm
14.3 cm

11.5 cm
11.5 cm

2.5 cm 

Answer 1

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

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

Given:

• Height (\(h\)) = 6 cm
• Diameter = 13 cm, so the radius (\(r\)) = \(\frac{13}{2} = 6.5\) cm

Now we can substitute the values into the Pythagorean Theorem:

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

Calculating \(6^2\) and \(6.5^2\):

\[ 6^2 = 36 \]

\[ 6.5^2 = 42.25 \]

Now, we can add these values:

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

Now we take the square root of both sides to find \(l\):

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

Rounding to the nearest tenth, the slant height is approximately 8.8 cm.

So the correct answer is:

8.8 cm