Question

Use the image to answer the 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

11.5 cm
11.5 cm

2.5 cm 
2.5 cm 
Skip to navigation

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the slant height, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the height of the cone is the perpendicular side, the radius (half of the diameter) is the base side, and the slant height is the hypotenuse.

From the image, we know that the diameter is 13 cm, so the radius is 13/2 = 6.5 cm.

Let's label the height as h, the slant height as L, and the radius as r.

Using the Pythagorean Theorem, we have:
L^2 = r^2 + h^2
L^2 = 6.5^2 + 6^2
L^2 = 42.25 + 36
L^2 = 78.25

Taking the square root of both sides, we get:
L = 8.8 cm

Therefore, the slant height must be approximately 8.8 cm.