What would be the slant length of a reducer transitioning from a 14" diameter to a 10" diameter, with a center length of 8"?

To determine the slant length of a reducer that transitions from a 14-inch diameter to a 10-inch diameter with a center length of 8 inches, you can employ the formula derived from the Pythagorean theorem. The slant length can be thought of as the hypotenuse of a right triangle, where the differences in diameter and the center length form the two other sides of the triangle.

First, calculate the difference in radius between the two diameters. The radius of the 14-inch diameter is 7 inches, and the radius of the 10-inch diameter is 5 inches. Therefore, the difference in radius is:

7 inches - 5 inches = 2 inches.

Next, you have the center length, which is 8 inches. You can now set up the right triangle:

• One leg is the difference in radius (2 inches).

• The other leg is the center length (8 inches).

Using the Pythagorean theorem, the slant length (hypotenuse) can be calculated as follows:

Slant Length = √(Difference in Radius² + Center Length²)

Substituting in the known values:

Slant Length = √(2² + 8²)

= √