The cross-section of a road cutting is drawn with x and y in metres…

Step 1. Meeting points. $\dfrac{x^2}{2} = x + 4$ gives $x^2 - 2x - 8 = 0$, so $(x - 4)(x + 2) = 0$ and $x = -2$ or $x = 4$.

Step 2. The area. The line is above the parabola. The area is $\displaystyle\int_{-2}^{4} \left(x + 4 - \dfrac{x^2}{2}\right) dx = \left[\dfrac{x^2}{2} + 4x - \dfrac{x^3}{6}\right]_{-2}^{4} = \dfrac{40}{3} + \dfrac{14}{3} = 18$.

Step 3. The volume. $18\ \text{m}^2 \times 50\ \text{m} = 900\ \text{m}^3$.