1. **Problem Statement:** We have two stations: 0+040 (fill) and 0+100 (cut). The ground line slopes uniformly at 5%. We know center heights, side slopes, and roadway widths. We need to find: a. Grade of finished road surface b. Area at station 0+040 c. Area at station 0+100 d. Volume of fill by end area method e. Volume of cut by end area method f. Whether the material is borrow or waste 2. **Grade of Finished Road Surface:** Grade is the slope of the finished road surface between stations. Given center heights: $h_1=1.40$ m at station 40 m, $h_2=2.80$ m at station 100 m. Distance between stations: $100 - 40 = 60$ m. Grade $= \frac{h_2 - h_1}{60} = \frac{2.80 - 1.40}{60} = \frac{1.40}{60} = 0.0233 = 2.33\%$ 3. **Area at Station 0+040 (Fill Section):** Formula for trapezoidal area: $$A = h \times \left(b + m h\right)$$ where $h$ is center height, $b$ is roadway width, $m$ is side slope ratio (horizontal to vertical). For fill: $h=1.40$ m, $b=9.00$ m, $m=2$ (2:1 side slope). Calculate side slope contribution: $m h = 2 \times 1.40 = 2.80$ m. Area: $$A = 1.40 \times (9.00 + 2.80) = 1.40 \times 11.80 = 16.52 \text{ m}^2$$ 4. **Area at Station 0+100 (Cut Section):** For cut: $h=2.80$ m, $b=10.00$ m, $m=1.5$ (1.5:1 side slope). Calculate side slope contribution: $m h = 1.5 \times 2.80 = 4.20$ m. Area: $$A = 2.80 \times (10.00 + 4.20) = 2.80 \times 14.20 = 39.76 \text{ m}^2$$ 5. **Volume by End Area Method:** Volume between two stations: $$V = \frac{L}{2} (A_1 + A_2)$$ where $L$ is distance between stations (60 m), $A_1$ and $A_2$ are areas at stations. - Volume of fill (station 0+040): $$V_{fill} = \frac{60}{2} (16.52 + 0) = 30 \times 16.52 = 495.6 \text{ m}^3$$ (Assuming zero area at start of fill section) - Volume of cut (station 0+100): $$V_{cut} = \frac{60}{2} (0 + 39.76) = 30 \times 39.76 = 1192.8 \text{ m}^3$$ (Assuming zero area at end of cut section) 6. **Borrow or Waste:** Since volume of cut (1192.8 m³) > volume of fill (495.6 m³), excess material is waste. **Final Answers:** a. Grade = 2.33% b. Area at 0+040 = 16.52 m² c. Area at 0+100 = 39.76 m² d. Volume of fill = 495.6 m³ e. Volume of cut = 1192.8 m³ f. Material is waste