Math Problem Statement

The pond in the local park has just been emptied and cleaned. The park attendants are trying to work out how many containers of water they will need to order. The pond is 6m long, 3000cm wide and 1.5m deep. The containers have a volume of 300cm cubed. How many containers are needed?

Solution

To solve this problem, we need to calculate the volume of the pond and then determine how many containers are required based on the volume of each container.

Step-by-Step Solution

  1. Calculate the Volume of the Pond:

    • Length of the pond = 6m=600cm6 \, \text{m} = 600 \, \text{cm}
    • Width of the pond = 3000cm3000 \, \text{cm}
    • Depth of the pond = 1.5m=150cm1.5 \, \text{m} = 150 \, \text{cm}
    • Volume of the pond = Length × Width × Depth Volume of the pond=600×3000×150=270,000,000cm3\text{Volume of the pond} = 600 \times 3000 \times 150 = 270{,}000{,}000 \, \text{cm}^3
  2. Calculate the Number of Containers Needed:

    • Volume of each container = 300cm3300 \, \text{cm}^3
    • Number of containers required = Volume of the pondVolume of each container\frac{\text{Volume of the pond}}{\text{Volume of each container}} Number of containers=270,000,000300=900,000\text{Number of containers} = \frac{270{,}000{,}000}{300} = 900{,}000

Answer

The number of containers needed is 900,000.

Would you like further details on this solution or have any other questions?

Here are five related questions to explore this concept further:

  1. How would the solution change if the depth of the pond were different?
  2. If each container could hold only 200 cm³ instead of 300 cm³, how many containers would be needed?
  3. How would the total number of containers change if the pond had a circular shape with the same volume?
  4. What if the dimensions were given in meters only? How would we approach the calculation?
  5. How could this problem be modified if some water already filled a portion of the pond?

Tip: Always ensure units are consistent throughout calculations, as mixing units can lead to incorrect results.

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Math Problem Analysis

Mathematical Concepts

Volume Calculation
Unit Conversion
Division for Quantity Determination

Formulas

Volume of a rectangular prism: Volume = Length × Width × Depth
Unit conversion from meters to centimeters
Number of containers = Total Volume / Volume of each container

Theorems

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Suitable Grade Level

Grades 7-9