The volume of a rectangular prism is $504 \mathrm{in}^{3}$ . Eric measures the sides to be $6$ . $63$ in by $7$ . $76$ in by $9$ . $08$ in. 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

504 \mathrm{in}^{3}

. Eric measures the sides to be

6

63

in by

7

76

in by

9

08

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

\newline

Answer:

Given: Given: $\newline$ Actual volume $V_{\text{actual}}$ = $504$ in $^3$ $\newline$ Measured sides: length $l$ = $6.63$ in, width $w$ = $7.76$ in, height $h$ = $9.08$ in $\newline$ First, calculate the volume using the measured sides. $\newline$ $V_{\text{measured}} = l \times w \times h$ $\newline$ $504$ $0$ in $504$ $1$ in $504$ $2$ in
Calculate volume: Perform the multiplication to find the measured volume. $\newline$ $V_{\text{measured}} = 6.63 \times 7.76 \times 9.08$ $\newline$ $V_{\text{measured}} = 467.04864 \text{ in}^3$
Find absolute error: Now, calculate the absolute error, which is the difference between the actual volume and the measured volume. $\newline$ Absolute error = $|V_{\text{actual}} - V_{\text{measured}}|$ $\newline$ Absolute error = $|504 - 467.04864|$
Calculate relative error: Subtract the measured volume from the actual volume to find the absolute error. $\newline$ Absolute error = $|504 - 467.04864|$ $\newline$ Absolute error = $36.95136$ in³
Express to nearest hundredth: Next, calculate the relative error, which is the absolute error divided by the actual volume. $\newline$ Relative error = $\frac{\text{Absolute error}}{V_{\text{actual}}}$ $\newline$ Relative error = $\frac{36.95136}{504}$
Express to nearest hundredth: Next, calculate the relative error, which is the absolute error divided by the actual volume. $\newline$ Relative error = $\frac{\text{Absolute error}}{V_{\text{actual}}}$ $\newline$ Relative error = $\frac{36.95136}{504}$ Perform the division to find the relative error. $\newline$ Relative error = $\frac{36.95136}{504}$ $\newline$ Relative error $\approx 0.073318$ in³/in³
Express to nearest hundredth: Next, calculate the relative error, which is the absolute error divided by the actual volume. $\newline$ Relative error = $\frac{\text{Absolute error}}{V_{\text{actual}}}$ $\newline$ Relative error = $\frac{36.95136}{504}$ Perform the division to find the relative error. $\newline$ Relative error = $\frac{36.95136}{504}$ $\newline$ Relative error $\approx 0.073318$ in³/in³Finally, express the relative error to the nearest hundredth. $\newline$ Relative error $\approx 0.07$ (to the nearest hundredth)