A 140-foot wide paved area is to be sloped 1/8 inch per foot. If the highest elevation at the center is 87.2 feet, what is the elevation at the lowest point at the perimeter?

A 140-foot wide paved area is to be sloped 1/8 inch per foot. If the highest elevation at the center is 87.2 feet, what is the elevation at the lowest point at the perimeter?

• A. 85.70 feet
• B. 86.50 feet
• C. 87.00 feet
• D. 88.10 feet

Answer: (B)

The change in elevation comes from the slope, which tells us how much height drops per horizontal distance. To get from the center to the edge, use half the width: 140 ft / 2 = 70 ft. The slope is 1/8 inch per foot, which is 0.125 inches of drop for every horizontal foot. Over 70 feet, the total drop is 70 × 0.125 = 8.75 inches. Convert that to feet: 8.75 inches ÷ 12 ≈ 0.729 ft. Subtract this from the center elevation: 87.2 ft − 0.729 ft ≈ 86.471 ft. Rounded to two decimals, about 86.47 ft, which is effectively 86.50 ft for the given options. Since the lowest point is at the perimeter, the edge elevation is the center elevation minus the drop.

The change in elevation comes from the slope, which tells us how much height drops per horizontal distance. To get from the center to the edge, use half the width: 140 ft / 2 = 70 ft. The slope is 1/8 inch per foot, which is 0.125 inches of drop for every horizontal foot. Over 70 feet, the total drop is 70 × 0.125 = 8.75 inches. Convert that to feet: 8.75 inches ÷ 12 ≈ 0.729 ft. Subtract this from the center elevation: 87.2 ft − 0.729 ft ≈ 86.471 ft. Rounded to two decimals, about 86.47 ft, which is effectively 86.50 ft for the given options. Since the lowest point is at the perimeter, the edge elevation is the center elevation minus the drop.