Chem tech makes paper cones used to filter liquids in lab experiments to make the paper cones that company starts with the net of the shape where the slant height is needed, the company wants the height of the cone to be 6 centimeters, if they make a diameter 13 centimeters, what must the slant height be? use the Pythagorean theorem and round the answer to the nearest 10th
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 (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the cone is the hypotenuse, the height is one of the other sides, and the radius (half the diameter) is the other side.
The height is given as 6 centimeters, and the diameter is 13 centimeters, so the radius is half of the diameter, or 13/2 = 6.5 centimeters.
Let's call the slant height "s".
Using the Pythagorean theorem, we can write the equation:
s^2 = 6^2 + 6.5^2
s^2 = 36 + 42.25
s^2 = 78.25
To solve for "s", we take the square root of both sides:
s ≈ √78.25
s ≈ 8.84
Rounding to the nearest tenth, the slant height of the cone should be approximately 8.8 centimeters.