To find the volume of the water trough, we can use the formula for the volume of a prism, which is the area of the base multiplied by the height (or in this case, the length of the trough).
The first step is to calculate the area of the trapezoidal cross-section. The formula for the area (A) of a trapezoid is:
A = (1/2) × (b1 + b2) × h
where b1 is the length of the bottom base, b2 is the length of the top base, and h is the height.
In this case:
- Bottom base (b1) = 30 cm
- Top base (b2) = 80 cm
- Height (h) = 50 cm
Converting everything to meters for consistency:
- Bottom base (b1) = 0.3 m
- Top base (b2) = 0.8 m
- Height (h) = 0.5 m
Substituting these values into the area formula:
A = (1/2) × (0.3 + 0.8) × 0.5 = (1/2) × 1.1 × 0.5 = 0.275 m²
Now that we have the area of the cross-section, we can calculate the volume of the trough. The length of the trough is 10 m, so:
Volume = Area × Length
Volume = 0.275 m² × 10 m = 2.75 m³
Thus, the volume of the water trough is 2.75 cubic meters.