The volume of a rectangular prism is $108 \mathrm{ft}^{3}$ . David measures the sides to be $6.14 \mathrm{ft}$ by $3.44 \mathrm{ft}$ by $5.8 \mathrm{ft}$ . In calculating the volume, what is the relative error, to the nearest hundredth. $\newline$ 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

108 \mathrm{ft}^{3}

. David measures the sides to be

6.14 \mathrm{ft}

3.44 \mathrm{ft}

5.8 \mathrm{ft}

. 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 $V_{\text{actual}}$ = $108$ ft³ $\newline$ - The measured dimensions are $6.14$ ft by $3.44$ ft by $5.8$ ft. $\newline$ First, we need to calculate the volume using the measured dimensions. $\newline$ $V_{\text{measured}} = \text{length} \times \text{width} \times \text{height}$ $\newline$ $V_{\text{measured}} = 6.14$ ft $\times 3.44$ ft $\times 5.8$ ft
Calculate Volume: Perform the multiplication to find the measured volume. $\newline$ $V_{\text{measured}} = 6.14 \times 3.44 \times 5.8$ $\newline$ $V_{\text{measured}} = 115.08704 \text{ ft}^3$
Find Absolute Error: Now, we calculate the absolute error, which is the difference between the actual volume and the measured volume. $\newline$ Absolute error = $|V_{\text{measured}} - V_{\text{actual}}|$ $\newline$ Absolute error = $|115.08704 \text{ ft}^3 - 108 \text{ ft}^3|$
Calculate Relative Error: Perform the subtraction to find the absolute error. $\newline$ Absolute error = $|115.08704 \text{ ft}³ - 108 \text{ ft}³|$ $\newline$ Absolute error = $|7.08704 \text{ ft}³|$
Round Relative Error: Next, we 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 = $\frac{7.08704 \, \text{ft}^3}{108 \, \text{ft}^3}$
Round Relative Error: Next, we 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 = $\frac{7.08704 \, \text{ft}^3}{108 \, \text{ft}^3}$ Perform the division to find the relative error. $\newline$ Relative error = $\frac{7.08704 \, \text{ft}^3}{108 \, \text{ft}^3}$ $\newline$ Relative error $\approx 0.06562037$
Round Relative Error: Next, we 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 = $\frac{7.08704 \text{ ft}^3}{108 \text{ ft}^3}$ Perform the division to find the relative error. $\newline$ Relative error = $\frac{7.08704 \text{ ft}^3}{108 \text{ ft}^3}$ $\newline$ Relative error $\approx 0.06562037$ Finally, we round the relative error to the nearest hundredth. $\newline$ Relative error $\approx 0.07$ (to the nearest hundredth)