Find the length of the height of the cone
13cm d=10cm
To find the height of a cone, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the cone is the hypotenuse, and the radius of the base is one of the other two sides. The height forms a right triangle with the radius and the slant height (which is the hypotenuse of the triangle formed by the height and the slant height).
Given that the diameter (d) of the cone is 10cm, we can find the radius (r) by dividing the diameter by 2:
r = d/2 = 10cm/2 = 5cm
Let h be the height of the cone.
Using the Pythagorean Theorem, we have:
r^2 + h^2 = slant height^2
Since the slant height is the hypotenuse of the right triangle formed by the height and the slant height, we can use the Pythagorean Theorem again to relate the height and the slant height.
The slant height (l) can be found by using the radius (r) and the height (h) as the other two sides of a right triangle:
l^2 = r^2 + h^2
Substituting the value of the radius:
l^2 = (5cm)^2 + h^2
l^2 = 25cm^2 + h^2
Since we're given that the diameter (d) is 10cm, we can find the slant height (l) by using the Pythagorean Theorem:
l = √(25cm^2 + h^2)
Therefore, the length of the height of the cone is given by the value of h. We would need more information or another equation to solve for h and find its exact length.