Full solution

Q. The volume of a rectangular prism is

80 \mathrm{~cm}^{3}

. Alex measures the sides to be

4.53 \mathrm{~cm}

2.02 \mathrm{~cm}

7.69 \mathrm{~cm}

. 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 $V_{\text{actual}}$ = $80$ cm³ $\newline$ - The measured dimensions of the prism are $4.53$ cm by $2.02$ cm by $7.69$ cm. $\newline$ First, we need to calculate the volume using the measured dimensions. $\newline$ $V_{\text{measured}} = \text{length} \times \text{width} \times \text{height}$
Calculate volume: Calculate the measured volume: $\newline$ $V_{\text{measured}} = 4.53 \, \text{cm} \times 2.02 \, \text{cm} \times 7.69 \, \text{cm}$ $\newline$ $V_{\text{measured}} = 70.300034 \, \text{cm}^3$
Calculate absolute error: Now, we find the absolute error, which is the difference between the actual volume and the measured volume. Absolute error = $|V_{\text{actual}} - V_{\text{measured}}|$
Calculate relative error: Calculate the absolute error: $\newline$ Absolute error = $\lvert 80 \, \text{cm}^3 - 70.300034 \, \text{cm}^3 \rvert$ $\newline$ Absolute error = $9.699966 \, \text{cm}^3$
Round relative error: Next, we calculate the relative error, which is the absolute error divided by the actual volume. $\newline$ Relative error $= \frac{\text{Absolute error}}{V_{\text{actual}}}$
Round relative error: Next, we calculate the relative error, which is the absolute error divided by the actual volume. $\newline$ Relative error = $\frac{\text{Absolute error}}{V_{\text{actual}}}$ Calculate the relative error: $\newline$ Relative error = $\frac{9.699966 \, \text{cm}^3}{80 \, \text{cm}^3}$ $\newline$ Relative error = $0.121249575$
Round relative error: Next, we calculate the relative error, which is the absolute error divided by the actual volume. $\newline$ Relative error $= \frac{\text{Absolute error}}{V_{\text{actual}}}$ Calculate the relative error: $\newline$ Relative error $= \frac{9.699966 \, \text{cm}^3}{80 \, \text{cm}^3}$ $\newline$ Relative error $= 0.121249575$ Finally, we round the relative error to the nearest hundredth. $\newline$ Relative error (rounded) $= 0.12$