Use the image to answer the question.
An illustration shows a right circular cylinder with an axis measuring 5 centimeters and diameter measuring 10 centimeters.
What is the height of the cylinder shown?
The height of the cylinder can be found using the Pythagorean theorem. The diameter of the cylinder is equal to the hypotenuse of a right triangle with the height as one of its legs and the radius as the other leg. The radius is half of the diameter, so it is 10/2 = 5 centimeters.
Using the Pythagorean theorem, we can write the equation:
Height^2 + (Radius)^2 = (Diameter)^2
Height^2 + 5^2 = 10^2
Height^2 + 25 = 100
Height^2 = 100 - 25
Height^2 = 75
Taking the square root of both sides, we find that the height is equal to the square root of 75, or approximately 8.66 centimeters.