High School

A toy company makes rectangular sand boxes that measure 2m by 1.5m by 0.6m. A customer bought the box and 2000000 cm³ of sand.

Determine the amount of sand the box can hold in cm³.

Answer :

To determine the amount of sand the box can hold, we first need to calculate the volume of the rectangular sandbox. The volume of a rectangular prism is determined by multiplying its length, width, and height. Let's go through the steps:

  1. Convert the Dimensions to Centimeters:

    • The dimensions of the sandbox are given in meters: 2 meters by 1.5 meters by 0.6 meters.
    • To work in cubic centimeters, convert the dimensions from meters to centimeters. Since 1 meter equals 100 centimeters:
      • Length: [tex]2 \times 100 = 200[/tex] cm
      • Width: [tex]1.5 \times 100 = 150[/tex] cm
      • Height: [tex]0.6 \times 100 = 60[/tex] cm

  2. Calculate the Volume of the Sandbox:

    • Use the formula for the volume of a rectangular prism:
      [tex]\text{Volume} = \text{length} \times \text{width} \times \text{height}[/tex]
    • Plug in the converted dimensions:
      [tex]\text{Volume} = 200 \times 150 \times 60[/tex]
    • Calculate:
      [tex]\text{Volume} = 1,800,000 \text{ cm}^3[/tex]

Therefore, the sandbox can hold [tex]1,800,000[/tex] cm³ of sand. This means the customer bought more sand ([tex]2,000,000[/tex] cm³) than can fit in the box, so some sand will be left over if they try to fill it entirely.

In conclusion, the sandbox can hold up to [tex]1,800,000[/tex] cm³ of sand.

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