Final answer:
To find the volume of the trapezoidal trough, calculate the cross-sectional area and multiply it by the length. The calculated volume is 90 cubic meters, which is not one of the options given, indicating an error in the question or options.
Step-by-step explanation:
The question involves finding the volume of a water trough with the shape of an isosceles trapezoidal cross-section. To calculate the volume of the trough, we use the formula for the volume of a prism, which is the cross-sectional area multiplied by the length of the prism. The cross-sectional area of an isosceles trapezoid can be found by using the formula A = (a + b) / 2 * h where 'a' and 'b' are the lengths of the parallel sides, and 'h' is the height.
The top width is 4 meters, the bottom width is 2 meters, and the height is 3 meters. The length of the trough is 10 meters. Applying the cross-sectional area formula, we get A = (4 + 2) / 2 * 3 = 3 * 3 = 9 m². Therefore, the volume is A * length = 9 m² * 10 m = 90 cubic meters, which is not one of the provided options. Hence, there may be an error in the question or the options provided.