Math Problem Statement

the height is 2.5m the width is 15

Solution

Thank you for the correction. Let's recalculate with the correct dimensions.

Updated Dimensions:

  • Height of the pool = 2.5 meters (instead of 1.5 meters)
  • Width of the pool = 15 meters (instead of 10 meters)

Part (a): Find the area of one side of the pool (shaded).

The shaded area is still a rectangle. With the corrected height, the area is:

Area=Length×Height=25m×2.5m=62.5m2\text{Area} = \text{Length} \times \text{Height} = 25 \, \text{m} \times 2.5 \, \text{m} = 62.5 \, \text{m}^2

Part (b): Find the volume of the pool in liters.

Using the corrected width, the volume is calculated as:

Volume=Length×Width×Depth=25m×15m×2.5m=937.5m3\text{Volume} = \text{Length} \times \text{Width} \times \text{Depth} = 25 \, \text{m} \times 15 \, \text{m} \times 2.5 \, \text{m} = 937.5 \, \text{m}^3

Now, convert this volume to liters:

Volume=937.5m3×1000L/m3=937,500L\text{Volume} = 937.5 \, \text{m}^3 \times 1000 \, \text{L/m}^3 = 937,500 \, \text{L}

Summary of Updated Results:

  • (a) The area of one side of the pool is 62.5 m².
  • (b) The volume of the pool is 937,500 liters.

Would you like to explore these results further or ask any questions?

Additional Questions:

  1. How does the increase in height affect the overall volume of the pool?
  2. If the width was only increased to 12 meters instead of 15 meters, what would be the new volume?
  3. What is the ratio of the area to the volume of the pool?
  4. How many liters of water are needed to fill 80% of the pool?
  5. What would be the area if the height was reduced by 1 meter?

Tip: Always double-check dimensions before calculations, as even small changes can significantly affect the final results, especially in volume-related problems.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume calculation
Unit conversion

Formulas

Volume of a rectangular prism: Volume = Length × Width × Height

Theorems

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Suitable Grade Level

High School