Final answer:
The perimeter of the intersection of the plane and the cone is 10π feet.
Step-by-step explanation:
To find the perimeter of the intersection of the plane and the cone, we can visualize the intersection as a shape similar to a circle. The radius of this circle is determined by the distance from the center of the circle to any point on the intersection. In this case, the height of the cone is 4 feet and the radius is 3 feet. Using the Pythagorean theorem, we can find the radius of the intersection to be 5 feet.
Since the intersection is circular, we can find the perimeter using the formula for the circumference of a circle: P = 2πr. Plugging in the radius of 5 feet, we get a perimeter of 2π(5) = 10π feet.