Find the length of the cone.
diameter = 10 cm
height = 13 cm
To find the length of the cone, we need to calculate the slant height.
The slant height (l) of a cone can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (l) is equal to the sum of the squares of the other two sides (r and h):
l^2 = r^2 + h^2
Given that the diameter is 10 cm, the radius (r) is half of that, which is 10/2 = 5 cm.
The height (h) is given as 13 cm.
Substituting these values into the equation, we get:
l^2 = 5^2 + 13^2
l^2 = 25 + 169
l^2 = 194
Taking the square root of both sides, we find:
l ≈ √194
l ≈ 13.928
Therefore, the length of the cone, or the slant height, is approximately 13.928 cm.