Final answer:
The slant height of the frustum of a cone can be found using the Pythagorean theorem. The slant height is equal to the square root of the sum of the squares of the difference in radii and the height of the frustum. We get 5 cm.
Step-by-step explanation:
In order to find the slant height of the frustum, we can use the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle, with the radius of the larger end (R) and the height of the frustum (h) as the other two sides.
Using the Pythagorean theorem, we have:
l² = (R - r)² + h²
Substituting the given values, we get:
l² = (5 - 2)² + 4²
l² = 9 + 16
l² = 25
l = √25
l = 5 cm