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Question

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.

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

11.5 cm
11.5 cm

2.5 cm 
2.5 cm 

14.3 cm
14.3 cm

 8.8 cm
 8.8 cm

Answer 1

To find the slant height of the cone using the Pythagorean Theorem, we can consider the dimensions given:

• The height (h) of the cone = 6 cm
• The diameter (d) of the base of the cone = 13 cm, so the radius (r) = d/2 = 13/2 = 6.5 cm

According to the Pythagorean Theorem, the relationship among the height (h), the radius (r), and the slant height (l) of the cone can be described with the equation:

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

Substituting the values into the equation:

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

Calculating \( (6.5)^2 \):

\[ (6.5)^2 = 42.25 \]

Calculating \( (6)^2 \):

\[ (6)^2 = 36 \]

Now, add these together:

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

Now take the square root to find \( l \):

\[ l = \sqrt{78.25} \approx 8.8 \]

Thus, the slant height \( l \) is approximately 8.8 cm.

The answer is:

8.8 cm