To find the slant height, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (slant height in this case) is equal to the sum of the squares of the other two sides. In this case, the slant height is the hypotenuse, the height is one side, and the radius (half the diameter) is the other side.
The radius of the cone is half the diameter, so it is 13 cm / 2 = 6.5 cm.
Using the Pythagorean theorem, we can find the slant height as follows:
(6.5 cm)^2 + (6 cm)^2 = slant height^2
42.25 cm^2 + 36 cm^2 = slant height^2
78.25 cm^2 = slant height^2
Taking the square root of both sides, we get:
slant height = √78.25 cm
slant height ≈ 8.8 cm
Therefore, the slant height of the cone should be approximately 8.8 cm.
Chem tech makes paper cones used to filter liquids and 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 to the nearest tenth
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