Find the length of the height of the cone
13 cm. d = 10 cm
To find the length of the 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 height of the cone is the perpendicular side, the diameter is the hypotenuse, and the radius (half the diameter) is one of the other two sides.
Let's call the radius "r". Since the diameter is 10 cm, the radius is half of that, which is 5 cm.
Now, using the Pythagorean Theorem, we can write:
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:
height = √75 = √(25 * 3) = √25 * √3 = 5√3
Therefore, the length of the height of the cone is 5√3 cm.