Question

A homeowner is putting in a fireplace that has a 2-inch-radius vent pipe. He needs to cut an elliptical hole in his roof to accommodate the pipe. If the pitch of his roof is 1/2 (a rise of 1, run of 2), what are the lengths of the major and minor axes of the ellipse? Round to two decimal places as needed. Use a comma to separate answers as needed.

Answer 1

The lengths of the major and minor axes of the ellipse are 4 inches and 2 inches, respectively.

Step-by-step explanation:

To find the lengths of the major and minor axes of the ellipse, we can use the information given. The vent pipe has a radius of 2 inches, so the diameter is 4 inches. The major axis of the ellipse will be equal to the diameter of the vent pipe, which is 4 inches. The minor axis can be found using the pitch of the roof, which is 1/2. Since the rise is 1 and the run is 2, the minor axis will be equal to the diameter of the vent pipe multiplied by the pitch, which is (4 inches) x (1/2) = 2 inches. Therefore, the lengths of the major and minor axes of the ellipse are 4 inches and 2 inches, respectively.