Got it! Let’s break down this problem step by step using the same format. This will help you understand how to calculate the amount of water needed to fill the pool to a specific depth.

Topic: Volume and Capacity of a Pool

Date: [Today’s Date]

Goal: Calculate the number of liters of water needed to fill a square pool to a depth of 50 cm.

Concept Explanation

Key Definitions

• Volume of a Pool: The amount of space inside the pool, which can be measured in cubic meters (m³).
• Cubic Meter: A cube with sides of 1 meter, equivalent to 1000 liters of water.
• Depth: The height of water the pool is filled to.

Step-by-Step Explanation

1. Find the Volume of the Pool
   The pool has sides of 3 meters, and we need to find its volume to a depth of 50 cm (0.5 meters). $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$ Given:

   • Length = 3 meters
   • Width = 3 meters (since it’s a square pool)
   • Height = 0.5 meters (depth)

   $\text{Volume} = 3 \, \text{m} \times 3 \, \text{m} \times 0.5 \, \text{m} = 4.5 \, \text{m}^3$

2. Convert Volume to Liters
   We know that 1 cubic meter equals 1000 liters. Therefore: $\text{Water Needed} = 4.5 \, \text{m}^3 \times 1000 \, \text{liters/m}^3 = 4500 \, \text{liters}$

Worked Example

Problem: A square pool has sides of 3 meters. One cubic meter holds 1000 liters of water. How many liters will it take to fill the pool to a depth of 50 cm?

Solution:

• Volume of the pool:
  $3 \, \text{m} \times 3 \, \text{m} \times 0.5 \, \text{m} = 4.5 \, \text{m}^3$
• Convert to liters:
  $4.5 \, \text{m}^3 \times 1000 = 4500 \, \text{liters}$

Answer: It will take 4500 liters of water to fill the pool to a depth of 50 cm.

Practice Problems

1. Easy: A pool has dimensions of 4 m by 4 m. If the depth is 1 meter, how many liters of water are needed to fill it?
2. Medium: A rectangular pool measures 6 m by 3 m and has a depth of 0.75 meters. How many liters of water does it hold?
3. Hard: A cylindrical pool has a radius of 2 meters and a depth of 2 meters. How many liters of water will fill the pool? (Use $\pi \approx 3.1416$)
4. Advanced: A pool has a trapezoidal shape with the following dimensions: the length is 10 meters, the width at the shallow end is 4 meters, and at the deep end, it is 6 meters. The depth is 2 meters. How many liters of water are needed?
5. Challenge: A pool is 8 meters long, 5 meters wide, and has a depth of 0.25 meters. How many liters of water will it take to fill the pool to half of its depth?

Mistake Journal

Problem: A square pool is 4 meters on each side and is filled to a depth of 1 meter. Calculate how many liters of water are needed.

Mistake: Incorrectly multiplied the volume by 500 instead of 1000 (1 cubic meter = 1000 liters).

Correct Solution:

• Volume:
  $4 \, \text{m} \times 4 \, \text{m} \times 1 \, \text{m} = 16 \, \text{m}^3$
• Convert to liters:
  $16 \, \text{m}^3 \times 1000 = 16,000 \, \text{liters}$

Reflection

• Key Takeaways:

  • Volume is found by multiplying the length, width, and depth of the pool.
  • Convert cubic meters to liters by multiplying by 1000.

• Next Steps:

  • Practice more volume calculations for various pool shapes.
  • Review the concept of converting between cubic units and liters.

Tip:

When dealing with volume and water capacity, always ensure you’re using the correct depth in meters (1 cm = 0.01 m), and remember that 1 cubic meter = 1000 liters.

Would you like further clarification or details on any of the steps?