Rainwater Harvesting System?

📌 CONCEPT: The problem requires us to find the point at which the rainwater should be poured to uniformly fill the tank, taking into account the trapezoidal shape of the tank's cross-section.

📐 RULE / FORMULA: We can use the concept of centroids to find the point at which the rainwater should be poured. The centroid of a trapezoid is the point where the medians intersect, and it divides each median into two segments with lengths in the ratio of the parallel sides. The distance from the base at which the rainwater should be poured is given by the formula: x = (h * (a + b)) / (2 * (a + b) + h), where x is the distance, h is the height, and a and b are the lengths of the parallel sides.

💡 WORKED EXAMPLE: Let's consider a trapezoid with parallel sides of length 10 m and 6 m, and a height of 3 m. Using the formula, we get: x = (3 * (10 + 6)) / (2 * (10 + 6) + 3) = (3 * 16) / (26) = 48 / 26 = 1.846 m. Therefore, the rainwater should be poured at a distance of approximately 1.846 m from the base.

⚠️ COMMON MISTAKE: Students often forget to consider the height of the tank when calculating the distance from the base at which the rainwater should be poured, which can lead to incorrect results.