Math Problem Statement

Calculate the volume of a box, in cubic centimeters, which is 423 cm long, 12 cm wide, and 25 cm high. Report your answer with correct significant figures in cubic centimeters.

Solution

To calculate the volume of a box, you can use the formula:

Volume=Length×Width×Height\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}

Given:

  • Length = 423 cm
  • Width = 12 cm
  • Height = 25 cm

Now, calculate the volume:

Volume=423cm×12cm×25cm\text{Volume} = 423 \, \text{cm} \times 12 \, \text{cm} \times 25 \, \text{cm}

Let's calculate that.The calculated volume of the box is 126,900 cubic centimeters.

To report the answer with the correct significant figures, we should consider the given measurements:

  • Length: 423 cm (3 significant figures)
  • Width: 12 cm (2 significant figures)
  • Height: 25 cm (2 significant figures)

The answer should be reported with the least number of significant figures, which is 2 significant figures. Therefore, the volume should be rounded to 2 significant figures.

The volume of the box is 130,000 cubic centimeters.

Would you like more details or have any questions? Here are five related questions you might find interesting:

  1. How does the volume change if the height is doubled?
  2. What is the volume of the box in liters?
  3. How would you find the surface area of the box?
  4. What is the volume in cubic meters?
  5. How would rounding rules affect the answer if different units were used?

Tip: When multiplying measurements with different significant figures, always round your final answer to match the measurement with the fewest significant figures.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume Calculation

Formulas

Volume of a box formula: Volume = Length × Width × Height

Theorems

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Suitable Grade Level

Grades 6-8