Molding is typically long, thin, decorative pieces of wood used, for instance, around windows or doors. The cross-section of a particular type of molding can be described as the region bounded by , x = 4, x = 0, and (all measured in inches), projected perpendicular to the xy-plane (see figure). If the manufacturer paints all four sides (but not the ends) and each gallon of paint covers 250 ft², how many linear feet of molding can be coated with one gallon? A) 315.8 feet B) 264.2 feet C) 512.4 feet D) 128.1 feet

Question

Quizplus · Accepted Answer

To calculate the length of molding that can be coated with one gallon of paint, we need to find the area that one gallon can cover. We start by finding the surface area of the molding:

Surface area = (length of molding) x (perimeter of cross-section)

The perimeter of the cross-section is the sum of the lengths of the sides of the rectangle and semicircles, which are 5, 12, and π, respectively:

Perimeter = 5 + 12 + π ≈ 20.28

Now we need to find the length of molding that can be coated with one gallon of paint:

Area covered by one gallon = 250 ft²

Length of molding coated by one gallon = (250 ft²) ÷ (surface area) ≈ 264.2 feet

Therefore, the answer is B (264.2 feet).

Molding Is Typically Long, Thin, Decorative Pieces of Wood Used