The volume of a rectangular prism is 144ft^(3). Alex measures the sides to be 2.63ft by 7.54ft by 6.13ft. In calculating the volume, what is the relative error, to the nearest thousandth. 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: Volume = length × width × height. Volume_calculated = 2.63 ft × 7.54 ft × 6.13 ft. Volume_calculated = 121.6742 ft³.Find absolute error: Now, we find the absolute error by subtracting the actual volume from the calculated volume. Absolute error = |Volume_actual - Volume_calculated|. Absolute error = |144 ft³ - 121.6742 ft³|. Absolute error = 22.3258 ft³.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. Relative error = (Absolute error / Volume_actual) × 100. Relative error = (22.3258 ft³ / 144 ft³) × 100. Relative error = 0.1550395833 × 100. Relative error = 15.50395833%.Round relative error: Finally, we round the relative error to the nearest thousandth. Relative error (rounded) = 15.504%.

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

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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Calculus

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

Full solution

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) = $15.504\%$ .