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 they make the diameter 13 cm what must the slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth
To find the slant height of the cone, 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, one side is the radius of the cone (half of the diameter), which is 13/2 = 6.5 cm.
The other side is the height of the cone, which is given as 6 cm.
Let's calculate the slant height:
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, we find:
slant height = √78.25 ≈ 8.8 cm
Therefore, the slant height of the cone should be approximately 8.8 cm.