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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

14.3 cm
14.3 cm

11.5 cm
11.5 cm

 8.8 cm
 8.8 cm

2.5 cm 

Answer 1

To find the slant height of the cone, we can use the Pythagorean Theorem. The slant height is the hypotenuse of a right triangle, where one leg is the height of the cone and the other leg is the radius of the base of the cone.

1. Find the radius: Given the diameter is 13 cm, the radius \( r \) is: \[ r = \frac{d}{2} = \frac{13 , \text{cm}}{2} = 6.5 , \text{cm} \]

2. Use the height: The height \( h \) of the cone is given as 6 cm.

3. Apply the Pythagorean Theorem: The formula is: \[ l = \sqrt{h^2 + r^2} \] where \( l \) is the slant height, \( h \) is the height, and \( r \) is the radius.

4. Substitute the values into the equation: \[ l = \sqrt{6^2 + 6.5^2} \] \[ l = \sqrt{36 + 42.25} \] \[ l = \sqrt{78.25} \] \[ l \approx 8.8 , \text{cm} \]

So, the slant height of the cone is approximately 8.8 cm.

The correct response is: 8.8 cm