To find the height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the diameter (D) of the base of the cone is 10 cm, so the radius (r) of the base is half of the diameter, or 5 cm. The height (h) of the cone is the unknown side we are trying to find.
Using the Pythagorean theorem, we can set up the equation:
r^2 + h^2 = D^2
Substituting the given values:
5^2 + h^2 = 13^2
25 + h^2 = 169
Subtracting 25 from both sides:
h^2 = 144
Taking the square root of both sides:
h = √144
h = 12 cm
Therefore, the length of the height of the cone is 12 cm.
Find the length of the height of the cone. D=10cm, 13cm
1 answer