The volume of a rectangular prism is $144 \mathrm{ft}^{3}$ . Alex measures the sides to be $2.63 \mathrm{ft}$ by $7.54 \mathrm{ft}$ by $6.13 \mathrm{ft}$ . In calculating the volume, what is the relative error, to the nearest thousandth. $\newline$ Answer:

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Find the rate of change of one variable when rate of change of other variable is given

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Q. The volume of a rectangular prism is

144 \mathrm{ft}^{3}

. Alex measures the sides to be

2.63 \mathrm{ft}

7.54 \mathrm{ft}

6.13 \mathrm{ft}

. In calculating the volume, what is the relative error, to the nearest thousandth.

\newline

Answer:

Given information: Given the volume of the rectangular prism is $144$ cubic feet, and Alex measures the sides to be $2.63$ feet, $7.54$ feet, and $6.13$ feet. To find the relative error, we first need to calculate the volume using Alex's measurements.
Calculate volume: Calculate the volume using Alex's measurements: $\text{Volume} = \text{length} \times \text{width} \times \text{height}$ . $\newline$ $\text{Volume}_{\text{calculated}} = 2.63 \, \text{ft} \times 7.54 \, \text{ft} \times 6.13 \, \text{ft}$ . $\newline$ $\text{Volume}_{\text{calculated}} = 121.6742 \, \text{ft}^3$ .
Find absolute error: Now, we find the absolute error by subtracting the actual volume from the calculated volume. $\newline$ Absolute error = $|\text{Volume}_{\text{actual}} - \text{Volume}_{\text{calculated}}|$ . $\newline$ Absolute error = $|144 \text{ ft}^3 - 121.6742 \text{ ft}^3|$ . $\newline$ Absolute error = $22.3258 \text{ ft}^3$ .
Find relative error: To find the relative error, we divide the absolute error by the actual volume and then multiply by $100$ to get the percentage. $\newline$ Relative error = $(\text{Absolute error} / \text{Volume}_{\text{actual}}) \times 100$ . $\newline$ Relative error = $(22.3258 \text{ ft}^3 / 144 \text{ ft}^3) \times 100$ . $\newline$ Relative error = $0.1550395833 \times 100$ . $\newline$ Relative error = $15.50395833\%$ .
Round relative error: Finally, we round the relative error to the nearest thousandth. $\newline$ Relative error (rounded) = $15.504\%$ .