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The volume of a rectangular prism is 90in^(3). Bob measures the sides to be 2.5 in by 2.52 in by 10.14 in. In calculating the volume, what is the relative error, to the nearest hundredth. Answer:

The volume of a rectangular prism is 90in3 90 \mathrm{in}^{3} . Bob measures the sides to be 22.55 in by 22.5252 in by 1010.1414 in. In calculating the volume, what is the relative error, to the nearest hundredth.\newlineAnswer:

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Q. The volume of a rectangular prism is 90in3 90 \mathrm{in}^{3} . Bob measures the sides to be 22.55 in by 22.5252 in by 1010.1414 in. In calculating the volume, what is the relative error, to the nearest hundredth.\newlineAnswer:
  1. Calculate Volume: Calculate the volume using the given side measurements.\newlineThe formula for the volume of a rectangular prism is length×width×height\text{length} \times \text{width} \times \text{height}.\newlineGiven measurements: length = 2.5 in2.5 \, \text{in}, width = 2.52 in2.52 \, \text{in}, height = 10.14 in10.14 \, \text{in}.\newlineVolume = 2.5 in×2.52 in×10.14 in2.5 \, \text{in} \times 2.52 \, \text{in} \times 10.14 \, \text{in}.\newlineVolume = 63.63 in363.63 \, \text{in}^3.
  2. Compare Volumes: Compare the calculated volume with the given volume. The given volume is 90 in390 \, \text{in}^3. The calculated volume is 63.63 in363.63 \, \text{in}^3.
  3. Calculate Absolute Error: Calculate the absolute error.\newlineAbsolute error = ∣Given volume−Calculated volume∣|\text{Given volume} - \text{Calculated volume}|.\newlineAbsolute error = ∣90 in3−63.63 in3∣|90 \text{ in}^3 - 63.63 \text{ in}^3|.\newlineAbsolute error = 26.37 in326.37 \text{ in}^3.
  4. Calculate Relative Error: Calculate the relative error.\newlineRelative error = (Absolute error/Given volume)×100(\text{Absolute error} / \text{Given volume}) \times 100.\newlineRelative error = (26.37 in3/90 in3)×100(26.37 \text{ in}^3 / 90 \text{ in}^3) \times 100.\newlineRelative error = 0.293×1000.293 \times 100.\newlineRelative error = 29.3%29.3\%.

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