Find the height of the cylinder. The radius is 5 cm and the diagonal is 15 cm
We have a right triangle formed by the height, radius, and diagonal of the cylinder. The radius and height are the legs of the triangle, and the diagonal is the hypotenuse.
Using the Pythagorean theorem, we can solve for the height:
height^2 + radius^2 = diagonal^2
height^2 + 5^2 = 15^2
height^2 + 25 = 225
height^2 = 225 - 25
height^2 = 200
Taking the square root of both sides:
height = √200
Therefore, the height of the cylinder is √200 cm.