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To solve the problem of finding the volume of the swimming pool, we can break it down step by step.

### Problem Description:
The pool has a trapezoidal cross-section. The dimensions provided are:
- Length (L): 50 meters
- Width (W): 21 meters
- Depth at one end: 0.8 meters
- Depth at the other end: 2.0 meters

### Step 1: Understanding the Shape of the Cross-Section
The cross-section of the pool is a trapezoid. The area \( A \) of a trapezoid is calculated using the formula:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where:
- \( b_1 \) and \( b_2 \) are the lengths of the parallel sides (depths of the pool),
- \( h \) is the height (width) of the trapezoid.

Here, \( b_1 = 0.8 \) meters, \( b_2 = 2.0 \) meters, and \( h = 21 \) meters.

### Step 2: Calculating the Cross-Sectional Area
Using the trapezoid area formula:
\[
A = \frac{1}{2} \times (0.8 + 2.0) \times 21
\]
Let's calculate this area.

### Step 3: Calculating the Volume of the Pool
Once we have the area of the trapezoidal cross-section, the volume \( V \) of the pool is given by:
\[
V = A \times L
\]
where \( L = 50 \) meters.

Let me calculate the exact values.The volume of the swimming pool is **1,470 cubic meters**.

Would you like more details or have any questions about the solution?

Here are 5 related questions to consider:
1. How would the volume change if the depth at the deeper end was 3 meters instead of 2 meters?
2. What is the surface area of the water at the top of the pool?
3. How much water (in liters) can the pool hold if it is filled to capacity?
4. If the pool is only filled to half its depth, what would be the new volume?
5. How long would it take to fill the pool if water is flowing in at a rate of 10 cubic meters per minute?

**Tip:** When dealing with geometric shapes like trapezoids, always double-check that you have the correct dimensions for the parallel sides and the height to ensure accurate area calculations.

The diagram shows a rectangular swimming pool which is 50 m long, 21 m wide, 0.8 m deep at one end and 2.0 m deep at the other end. Find the volume of the pool.

Find the volume of a rectangular swimming pool with a trapezoidal cross-section. The pool is 50 meters long, 21 meters wide, with depths of 0.8 meters and 2.0 meters at opposite ends. Learn how to calculate the area of a trapezoid and the volume of the pool, suitable for students in Grades 7-9.

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