Answer:
To find the slant height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
In this case, the height of the cone (h) is one of the legs of the right triangle, and the radius of the cone (r) is the other leg. The slant height (s) is the hypotenuse.
Using the Pythagorean theorem, we have:
s^2 = h^2 + r^2
Substituting the given values, we have:
s^2 = 12^2 + 9^2
s^2 = 144 + 81
s^2 = 225
Taking the square root of both sides, we find:
s = √225
s = 15 cm
Therefore, the slant height of the cone is 15 centimeters (cm).
Step-by-step explanation: