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
8.8 cm
8.8 cm
2.5 cm
2.5 cm
14.3 cm
14.3 cm
11.5 cm
To answer this question, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diameter of the cone is the base of the right triangle, and the height of the cone is the other side. The slant height is the hypotenuse.
Let's call the slant height "s", the diameter "d", and the height "h".
According to the Pythagorean Theorem, we have the equation:
s^2 = d^2 + h^2
In this question, the diameter is given as 13 cm, and the height is given as 6 cm.
Plugging the values into the equation, we get:
s^2 = 13^2 + 6^2
s^2 = 169 + 36
s^2 = 205
To find the slant height, we need to take the square root of both sides:
s = √205
s ≈ 14.3 cm
Therefore, the slant height must be approximately 14.3 cm.
The correct answer is:
14.3 cm