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The volume of a rectangular prism is 140in^(3). Carter measures the sides to be 2.22 in by 10 in by 6.59in. In calculating the volume, what is the relative error, to the nearest thousandth. Answer:

The volume of a rectangular prism is 140in3 140 \mathrm{in}^{3} . Carter measures the sides to be 22.2222 in by 1010 in by 6.59in 6.59 \mathrm{in} . 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 140in3 140 \mathrm{in}^{3} . Carter measures the sides to be 22.2222 in by 1010 in by 6.59in 6.59 \mathrm{in} . In calculating the volume, what is the relative error, to the nearest thousandth.\newlineAnswer:
  1. Calculate Volume: Calculate the volume using the measured sides.\newlineThe formula for the volume of a rectangular prism is V=length×width×heightV = \text{length} \times \text{width} \times \text{height}.\newlineUsing Carter's measurements, we calculate the volume as follows:\newlineV=2.22 in×10 in×6.59 inV = 2.22 \, \text{in} \times 10 \, \text{in} \times 6.59 \, \text{in}.
  2. Perform Multiplication: Perform the multiplication to find the calculated volume.\newlineVcalculated=2.22×10×6.59.V_{\text{calculated}} = 2.22 \times 10 \times 6.59.\newlineVcalculated=146.358 in3.V_{\text{calculated}} = 146.358 \text{ in}^3.
  3. Compare Volumes: Compare the calculated volume with the given volume.\newlineThe given volume is Vgiven=140V_{\text{given}} = 140 in3^3.\newlineThe calculated volume from Step 22 is Vcalculated=146.358V_{\text{calculated}} = 146.358 in3^3.
  4. Calculate Absolute Error: Calculate the absolute error.\newlineAbsolute error = ∣Vcalculated−Vgiven∣|V_{\text{calculated}} - V_{\text{given}}|.\newlineAbsolute error = ∣146.358−140∣|146.358 - 140|.\newlineAbsolute error = 6.3586.358 in³.
  5. Calculate Relative Error: Calculate the relative error.\newlineRelative error = (Absolute error/Vgiven)×100%(\text{Absolute error} / V_{\text{given}}) \times 100\%.\newlineRelative error = (6.358/140)×100%(6.358 / 140) \times 100\%.
  6. Convert Relative Error: Perform the division and multiplication to find the relative error.\newlineRelative error = (6.358/140)×100(6.358 / 140) \times 100.\newlineRelative error ≈0.04541428571×100\approx 0.04541428571 \times 100.\newlineRelative error ≈4.541428571%\approx 4.541428571\%.
  7. Convert Relative Error: Perform the division and multiplication to find the relative error.\newlineRelative error = (6.358/140)×100(6.358 / 140) \times 100.\newlineRelative error ≈0.04541428571×100\approx 0.04541428571 \times 100.\newlineRelative error ≈4.541428571%\approx 4.541428571\%.Convert the relative error to the nearest thousandth.\newlineRelative error ≈4.541%\approx 4.541\%.\newlineTo express this as a decimal to the nearest thousandth, we divide by 100100 and round to three decimal places.\newlineRelative error ≈0.045\approx 0.045 (rounded to three decimal places).

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