The Pythagorean Theorem in Three Dimensions Quick Check
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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
11.5 cm
11.5 cm
14.3 cm
14.3 cm
2.5 cm
2.5 cm
8.8 cm
8.8 cm
To find the slant height, we can use the Pythagorean Theorem, which states that for a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
Let the height of the cone be 6 cm and the diameter be 13 cm. The radius of the circle (which is half the diameter) would be 6.5 cm.
Using the Pythagorean Theorem:
slant height^2 = radius^2 + height^2
slant height^2 = 6.5^2 + 6^2
slant height^2 = 42.25 + 36
slant height^2 = 78.25
Taking the square root of both sides to find the slant height:
slant height = √78.25
slant height ≈ 8.8 cm
Therefore, the slant height of the cone should be approximately 8.8 cm. The answer is 8.8 cm.