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The volume of a rectangular prism is
270in^(3). Alex measures the sides to be 5.71 in by 5.46 in by 9.4 in. In calculating the volume, what is the relative error, to the nearest hundredth.
Answer:

The volume of a rectangular prism is $270 \mathrm{in}^{3}$ . Alex measures the sides to be $5$ . $71$ in by $5$ . $46$ in by $9$ . $4$ in. In calculating the volume, what is the relative error, to the nearest hundredth. $\newline$ Answer:

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Circles: word problems

Full solution

Q. The volume of a rectangular prism is

270 \mathrm{in}^{3}

. Alex measures the sides to be

5

.

71

in by

5

.

46

in by

9

.

4

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

\newline

Answer:

Calculate Volume: Calculate the volume of the rectangular prism using the given measurements. $\newline$ Volume = Length $\times$ Width $\times$ Height $\newline$ Volume = $5.71$ in $\times$ $5.46$ in $\times$ $9.4$ in $\newline$ Volume = $293.0204$ in $^3$
Find Absolute Error: Compare the calculated volume with the given volume to find the absolute error. $\newline$ Absolute error = $|\text{Calculated Volume} - \text{Given Volume}|$ $\newline$ Absolute error = $|293.0204 \text{ in}^3 - 270 \text{ in}^3|$ $\newline$ Absolute error = $23.0204 \text{ in}^3$
Calculate Relative Error: Calculate the relative error by dividing the absolute error by the given volume and then converting it to a percentage. $\newline$ Relative error = $(\text{Absolute error} / \text{Given Volume}) \times 100\%$ $\newline$ Relative error = $(23.0204 \text{ in}^3 / 270 \text{ in}^3) \times 100\%$ $\newline$ Relative error = $0.08526 \times 100\%$ $\newline$ Relative error = $8$ . $526$ \%
Round Relative Error: Round the relative error to the nearest hundredth. $\newline$ Relative error (rounded) = $8.53\%$

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