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The volume of a rectangular prism is
150in^(3). Alex measures the sides to be 2.8 in by 9.72 in by 4.54 in. In calculating the volume, what is the relative error, to the nearest hundredth.
Answer:

The volume of a rectangular prism is $150 \mathrm{in}^{3}$ . Alex measures the sides to be $2$ . $8$ in by $9$ . $72$ in by $4$ . $54$ in. 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

Full solution

Q. The volume of a rectangular prism is

150 \mathrm{in}^{3}

. Alex measures the sides to be

2

.

8

in by

9

.

72

in by

4

.

54

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

\newline

Answer:

Given: Given: $\newline$ Volume of rectangular prism $V$ = $150$ cubic inches $\newline$ Measured sides are $2.8$ in, $9.72$ in, and $4.54$ in. $\newline$ First, calculate the volume using the measured sides. $\newline$ Volume $V_{\text{measured}}$ = length $\times$ width $\times$ height $\newline$ $V_{\text{measured}} = 2.8$ in $\times 9.72$ in $150$ $0$ in $\newline$ $150$ $1$ in $150$ $2$
Calculate Volume: Next, calculate the absolute error, which is the difference between the true volume and the measured volume. $\newline$ Absolute error = $|V - V_{\text{measured}}|$ $\newline$ Absolute error = $|150 \text{ in}^3 - 123.8496 \text{ in}^3|$ $\newline$ Absolute error = $26.1504 \text{ in}^3$
Calculate Absolute Error: Now, calculate the relative error, which is the absolute error divided by the true volume. $\newline$ Relative error = $\frac{\text{Absolute error}}{V}$ $\newline$ Relative error = $\frac{26.1504 \, \text{in}^3}{150 \, \text{in}^3}$ $\newline$ Relative error = $0.174336$
Calculate Relative Error: Finally, express the relative error to the nearest hundredth. $\newline$ Relative error (to the nearest hundredth) = $0.17$

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