The volume of a rectangular prism is $90 \mathrm{in}^{3}$ . Bob measures the sides to be $2$ . $5$ in by $2$ . $52$ in by $10$ . $14$ in. In calculating the volume, what is the relative error, to the nearest hundredth. $\newline$ Answer:

Full solution

Q. The volume of a rectangular prism is

90 \mathrm{in}^{3}

. Bob measures the sides to be

2

5

in by

2

52

in by

10

14

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

\newline

Answer:

Calculate Volume: Calculate the volume using the given side measurements. $\newline$ The formula for the volume of a rectangular prism is $\text{length} \times \text{width} \times \text{height}$ . $\newline$ Given measurements: length = $2.5 \, \text{in}$ , width = $2.52 \, \text{in}$ , height = $10.14 \, \text{in}$ . $\newline$ Volume = $2.5 \, \text{in} \times 2.52 \, \text{in} \times 10.14 \, \text{in}$ . $\newline$ Volume = $63.63 \, \text{in}^3$ .
Compare Volumes: Compare the calculated volume with the given volume. The given volume is $90 \, \text{in}^3$ . The calculated volume is $63.63 \, \text{in}^3$ .
Calculate Absolute Error: Calculate the absolute error. $\newline$ Absolute error = $|\text{Given volume} - \text{Calculated volume}|$ . $\newline$ Absolute error = $|90 \text{ in}^3 - 63.63 \text{ in}^3|$ . $\newline$ Absolute error = $26.37 \text{ in}^3$ .
Calculate Relative Error: Calculate the relative error. $\newline$ Relative error = $(\text{Absolute error} / \text{Given volume}) \times 100$ . $\newline$ Relative error = $(26.37 \text{ in}^3 / 90 \text{ in}^3) \times 100$ . $\newline$ Relative error = $0.293 \times 100$ . $\newline$ Relative error = $29.3\%$ .