Math Problem Statement
A box measures 3.12 ft in length, 0.0455 yd in width, and 7.87 inches in height. What is its volume in mm^3 if the volume with correct sig figs?
Solution
To calculate the volume of the box, we first need to convert all measurements to the same unit (millimeters, mm) and then compute the volume using the formula for the volume of a rectangular box:
Step 1: Convert all measurements to millimeters (mm)
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Length: 3.12 feet to millimeters
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Width: 0.0455 yards to millimeters
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Height: 7.87 inches to millimeters
Step 2: Calculate the volume in cubic millimeters
Now, let's compute the volume and round to the correct number of significant figures. The least number of significant figures in the given measurements is 3 (from the width: 0.0455).
Step 3: Perform the calculation
Let's calculate the volume:
The converted dimensions in millimeters are:
- Length:
- Width:
- Height:
Volume Calculation
Step 4: Round to the Correct Significant Figures
The measurement with the fewest significant figures is 0.0455 (3 significant figures). Thus, the volume should be rounded to 3 significant figures:
Final Answer
The volume of the box, with the correct number of significant figures, is .
Would you like more details or have any questions? Here are 5 related questions for further exploration:
- How do you convert between different units of volume?
- What are significant figures, and why are they important in calculations?
- How would you calculate the surface area of this box?
- How does dimensional analysis help in unit conversions?
- What other physical properties could be calculated for this box using its dimensions?
Tip: Always check the number of significant figures when converting units to ensure precision and accuracy in scientific calculations.
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Math Problem Analysis
Mathematical Concepts
Unit Conversion
Volume Calculation
Significant Figures
Formulas
Volume of a Rectangular Box: V = length × width × height
Theorems
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Suitable Grade Level
High School
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