To find the slant height of the cone, we can use the Pythagorean Theorem. The height of the cone is given as 6 cm and the diameter is given as 13 cm.
We can divide the diameter by 2 to find the radius of the cone, which is 6.5 cm.
Now we can use the Pythagorean Theorem, with the radius as one leg, the slant height as the other leg, and the hypotenuse as the diameter (which is twice the radius).
Using this, we have:
(6.5)^2 + slant height^2 = 13^2
42.25 + slant height^2 = 169
slant height^2 = 169 - 42.25
slant height^2 = 126.75
slant height = √126.75
slant height ≈ 11.3 cm
Rounding to the nearest tenth, the slant height of the cone should be approximately 11.5 cm.
Therefore, the correct answer is 11.5 cm.
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
11.5 cm
11.5 cm
8.8 cm
8.8 cm
2.5 cm
2.5 cm
14.3 cm
14.3 cm
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1 answer
1 answer