Concept explainers
A sidewalk is to be constructed around a swimming pool that measures (10.0 ± 0.1) m by (17.0 ± 0.1) m. If the sidewalk is to measure (1.00 ± 0.01) m wide by (9.0 ± 0.1) cm thick, what volume of concrete is needed and what is the approximate uncertainty of this volume?
The required volume of concrete and approximate uncertainty of the volume.
Answer to Problem 1.53P
The required volume of concrete is
Explanation of Solution
Given info: The length of swimming pool is
The length of the side walk in long side is,
The total length in small side is,
Formula to calculate the volume of rectangle in long side is,
Here,
Substitute
Thus, the volume of rectangle in long side is
Formula to calculate the volume of rectangle in small side is,
Substitute
Thus, the volume of rectangle in small side is
Write the expression for total volume of the concrete needed,
Substitute
Thus, the total volume of concrete required is
The uncertainty of the volume is the sum of uncertainty in each dimension.
The total length with uncertainty in the long side is,
The total length with uncertainty in small side is,
Formula to calculate the volume with uncertainty in long side is,
Here,
Substitute
Thus, the volume with uncertainty in long side is
Formula to calculate the volume with uncertainty in small side is,
Substitute
Thus, the volume with uncertainty in small side is
Write the expression for total volume with uncertainty,
Substitute
The total volume with uncertainty is
Write the expression for the uncertainty in the volume,
Substitute
Thus, the uncertainty in volume is
Conclusion:
Therefore, the required volume of concrete is
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