Using the Pythagorean Theorem, we can find the slant height of the cone by using the diameter and height of the cone.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the diameter (d) is the hypotenuse, and the height (h) is one of the sides.
Using the given information:
diameter (d) = 13 cm
height (h) = 6 cm
We need to find the slant height (s).
To apply the Pythagorean Theorem:
d^2 = h^2 + s^2
Substituting the given values:
(13 cm)^2 = (6 cm)^2 + s^2
Simplifying:
169 cm^2 = 36 cm^2 + s^2
Subtracting 36 cm^2 from both sides:
133 cm^2 = s^2
Taking the square root of both sides:
s ≈ √133
s ≈ 11.5 cm
Therefore, the slant height of the cone should be approximately 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.
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