AL athletes makes poles for pole vaulting They use cylinder-shaped containers for shipping. If the company is mailing a pole that is 10 ft in length in a container that has a height of 8 ft what radius is needed for the pole to fit perfectly on the diagonal
We can use the Pythagorean theorem to solve this problem.
The diagonal of the container can be thought of as the hypotenuse of a right triangle, with the height of the container as one side and the radius of the pole as the other side. The length of the pole is the diagonal.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (height)^2 + (radius)^2
(10 ft)^2 = (8 ft)^2 + (radius)^2
100 ft^2 = 64 ft^2 + (radius)^2
Subtracting 64 ft^2 from both sides:
36 ft^2 = (radius)^2
Taking the square root of both sides:
6 ft = radius
Therefore, a radius of 6 ft is needed for the pole to fit perfectly on the diagonal.