https://file.aiquickdraw.com/mathbot/file/1730710754125ety2onhk.jpg

To solve this problem, let's break down each part:

### Given Information
1. **Volume of the swimming pool**: \( V = 8.57 \, \text{m}^3 \)
2. **Inner radius of each half-cylinder**: \( r = 1 \, \text{m} \)
3. **Total length of the pool (including the half-cylinders)**: \( 2 \, \text{m} \)

The pool consists of:
- A rectangular prism section in the middle.
- Two half-cylinders on each end.

### Part 5.1: Calculate the Depth of the Swimming Pool (\( h \))

Since the pool has a volume of \( 8.57 \, \text{m}^3 \), we can set up an equation for the total volume using the volume of the rectangular prism and the two half-cylinders.

#### Step 1: Volume of the Rectangular Prism
The rectangular prism has:
- **Length** \( l = 2 - 2 \times 1 = 0 \, \text{m} \) (this calculation appears incorrect; instead, we should calculate for the central section as given in the diagram).



The diagram below shows a swimming pool with a volume of 8.57 m³ and an inner radius of 1 m. The swimming pool is made out of a rectangular prism and has two half-cylinders at each end. Ignore the thickness of the swimming pool. Calculate: 5.1 The depth of the swimming pool. 5.2 The surface area of the bottom of the swimming pool to repaint it.

Solve for the depth and bottom surface area of a swimming pool made up of a rectangular prism with two half-cylinders, given a total volume of 8.57 m³ and radius of 1 m. This problem involves geometry concepts including volume and surface area calculations, suitable for students in Grades 10-12.

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