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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

 8.8 cm
 8.8 cm

14.3 cm
14.3 cm

2.5 cm 
2.5 cm 

11.5 cm

Answer 1

To find the slant height of the cone, you can use the Pythagorean theorem. The cone's slant height, height, and radius form a right triangle.

1. First, find the radius of the cone. The diameter is given as 13 cm, so the radius \( r \) is: \[ r = \frac{d}{2} = \frac{13 , \text{cm}}{2} = 6.5 , \text{cm} \]

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

3. According to the Pythagorean theorem: \[ s^2 = r^2 + h^2 \] where \( s \) is the slant height.

4. Substitute the known values into the equation: \[ s^2 = (6.5 , \text{cm})^2 + (6 , \text{cm})^2 \] \[ s^2 = 42.25 , \text{cm}^2 + 36 , \text{cm}^2 \] \[ s^2 = 78.25 , \text{cm}^2 \]

5. Now, take the square root to find the slant height \( s \): \[ s = \sqrt{78.25} \approx 8.8 , \text{cm} \]

So the slant height must be approximately 8.8 cm.

The correct response is: 8.8 cm.