The volume of a rectangular prism is $360 \mathrm{~cm}^{3}$ . Alex measures the sides to be $9.09 \mathrm{~cm}$ by $4.84 \mathrm{~cm}$ by $8.35 \mathrm{~cm}$ . In calculating the volume, what is the relative error, to the nearest hundredth. $\newline$ Answer:

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Q. The volume of a rectangular prism is

360 \mathrm{~cm}^{3}

. Alex measures the sides to be

9.09 \mathrm{~cm}

4.84 \mathrm{~cm}

8.35 \mathrm{~cm}

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

\newline

Answer:

Given: Given: $\newline$ The actual volume of the rectangular prism $V_{\text{actual}}$ = $360\,\text{cm}^3$ $\newline$ Measured dimensions: length $l$ = $9.09\,\text{cm}$ , width $w$ = $4.84\,\text{cm}$ , height $h$ = $8.35\,\text{cm}$ $\newline$ Calculate the measured volume $V_{\text{measured}}$ using the measured dimensions. $\newline$ $V_{\text{measured}} = l \times w \times h$ $\newline$ $360\,\text{cm}^3$ $0$
Calculate Volume: Perform the multiplication to find the measured volume. $\newline$ $V_{\text{measured}} = 9.09 \, \text{cm} \times 4.84 \, \text{cm} \times 8.35 \, \text{cm}$ $\newline$ $V_{\text{measured}} = 367.03914 \, \text{cm}^3$
Perform Multiplication: Calculate the absolute error, which is the difference between the measured volume and the actual volume. $\newline$ Absolute error = $|V_{\text{measured}} - V_{\text{actual}}|$ $\newline$ Absolute error = $|367.03914 \, \text{cm}^3 - 360 \, \text{cm}^3|$ $\newline$ Absolute error = $7.03914 \, \text{cm}^3$
Calculate Absolute Error: Calculate the relative error by dividing the absolute error by the actual volume and then multiplying by $100$ to get the percentage. $\text{Relative error} = \frac{\text{Absolute error}}{V_{\text{actual}}} \times 100$ $\text{Relative error} = \frac{7.03914 \, \text{cm}^3}{360 \, \text{cm}^3} \times 100$
Calculate Relative Error: Perform the division and multiplication to find the relative error. $\newline$ Relative error = $(7.03914 \, \text{cm}^3 / 360 \, \text{cm}^3) \times 100$ $\newline$ Relative error = $0.01955317 \times 100$ $\newline$ Relative error = $1.955317\%$
Round Relative Error: Round the relative error to the nearest hundredth. $\newline$ Relative error $\approx 1.96\%$