Certainly! Let's calculate the number of balls that can be packed into the truck step by step.
### Step 1: Understanding the Dimensions
- Box Dimensions: The dimensions of each box are given as 1200 mm by 100 cm by 100 cm.
- Convert all measurements to millimeters (mm) since we need uniform units for accurate calculations.
- [tex]\(1200\)[/tex] mm is already in millimeters.
- [tex]\(100\)[/tex] cm converted to millimeters: [tex]\(100 \text{ cm} \times 10 \frac{\text{mm}}{\text{cm}} = 1000 \text{ mm}\)[/tex]
- Therefore, the box dimensions are [tex]\(1200 \text{ mm}\)[/tex] by [tex]\(1000 \text{ mm}\)[/tex] by [tex]\(1000 \text{ mm}\)[/tex].
- Truck Dimensions: The truck dimensions are given as [tex]\(6 \text{ m}\)[/tex] by [tex]\(2500 \text{ m}\)[/tex] by [tex]\(180 \text{ cm}\)[/tex].
- Convert all measurements to millimeters (mm):
- [tex]\(6 \text{ m} \times 1000 \frac{\text{mm}}{\text{m}} = 6000 \text{ mm}\)[/tex]
- [tex]\(2500 \text{ m} \times 1000 \frac{\text{mm}}{\text{m}} = 2500000 \text{ mm}\)[/tex]
- [tex]\(180 \text{ cm} \times 10 \frac{\text{mm}}{\text{cm}} = 1800 \text{ mm}\)[/tex]
- Thus, the truck dimensions are [tex]\(6000 \text{ mm}\)[/tex] by [tex]\(2500000 \text{ mm}\)[/tex] by [tex]\(1800 \text{ mm}\)[/tex].
### Step 2: Calculate the Volume
- Volume of the Box:
- Using the formula for the volume of a rectangular prism ([tex]\( \text{length} \times \text{width} \times \text{height} \)[/tex]):
- Volume = [tex]\(1200 \text{ mm} \times 1000 \text{ mm} \times 1000 \text{ mm} = 1200000000 \text{ mm}^3\)[/tex]
- Volume of the Truck:
- Similarly, using the same volume formula for the truck:
- Volume = [tex]\(6000 \text{ mm} \times 2500000 \text{ mm} \times 1800 \text{ mm} = 27000000000000 \text{ mm}^3\)[/tex]
### Step 3: Calculate the Number of Boxes
- To find out how many boxes can fit into the truck, divide the total volume of the truck by the volume of one box:
- [tex]\(\text{Number of Boxes} = \frac{\text{Truck Volume}}{\text{Box Volume}} = \frac{27000000000000 \text{ mm}^3}{1200000000 \text{ mm}^3}\)[/tex]
- By performing the division, we get [tex]\(\text{Number of Boxes} = 22500\)[/tex]
### Conclusion
The number of balls that can be packed in this truck is 22,500.
