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The volume of a rectangular prism is 500cm^(3). Bob measures the sides to be 10.35cm by 10.06cm by 4.92cm. In calculating the volume, what is the relative error, to the nearest thousandth. Answer:

The volume of a rectangular prism is 500 cm3 500 \mathrm{~cm}^{3} . Bob measures the sides to be 10.35 cm 10.35 \mathrm{~cm} by 10.06 cm 10.06 \mathrm{~cm} by 4.92 cm 4.92 \mathrm{~cm} . In calculating the volume, what is the relative error, to the nearest thousandth.\newlineAnswer:

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Q. The volume of a rectangular prism is 500 cm3 500 \mathrm{~cm}^{3} . Bob measures the sides to be 10.35 cm 10.35 \mathrm{~cm} by 10.06 cm 10.06 \mathrm{~cm} by 4.92 cm 4.92 \mathrm{~cm} . In calculating the volume, what is the relative error, to the nearest thousandth.\newlineAnswer:
  1. Calculate Volume: Calculate the volume using the given measurements.\newlineTo find the volume of a rectangular prism, multiply the length by the width by the height.\newlineVolume = length ×\times width ×\times height\newlineVolume = 10.35 cm×10.06 cm×4.92 cm10.35\,\text{cm} \times 10.06\,\text{cm} \times 4.92\,\text{cm}\newlineVolume = 511.11732 cm3511.11732\,\text{cm}^3
  2. Find Absolute Error: Find the absolute error by subtracting the actual volume from the calculated volume.\newlineAbsolute error = ∣Calculated volume−Actual volume∣\lvert\text{Calculated volume} - \text{Actual volume}\rvert\newlineAbsolute error = ∣511.11732 cm3−500 cm3∣\lvert511.11732\,\text{cm}^3 - 500\,\text{cm}^3\rvert\newlineAbsolute error = 11.11732 cm311.11732\,\text{cm}^3
  3. Find Relative Error: Find the relative error by dividing the absolute error by the actual volume.\newlineRelative error = Absolute errorActual volume\frac{\text{Absolute error}}{\text{Actual volume}}\newlineRelative error = 11.11732 cm3500 cm3\frac{11.11732\,\text{cm}^3}{500\,\text{cm}^3}\newlineRelative error = 0.022234640.02223464
  4. Convert to Percentage: Convert the relative error to a percentage and round to the nearest thousandth.Relativeerror(tothenearestthousandth)=0.022Relative error (to the nearest thousandth) = 0.022

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