Find the length of the cone.
slant height= 13cm
d= 10cm
To find the length of the cone, we can use the Pythagorean Theorem. The slant height of the cone is the hypotenuse of a right triangle, with the radius of the base as one leg and the height of the cone as the other leg. We are given the slant height (13 cm) and the radius of the base (diameter of 10 cm, so radius of 5 cm).
Using the Pythagorean Theorem, we can set up the equation:
(5 cm)^2 + height^2 = (13 cm)^2
Simplifying,
25 cm^2 + height^2 = 169 cm^2
Subtracting 25 cm^2 from both sides,
height^2 = 169 cm^2 - 25 cm^2
height^2 = 144 cm^2
Taking the square root of both sides,
height = √144 cm
height = 12 cm
Therefore, the length of the cone (height) is 12 cm.