The volume of a rectangular prism is 80cm^(3). Alex measures the sides to be 4.53cm by 2.02cm by 7.69cm. In calculating the volume, what is the relative error, to the nearest hundredth. Answer:

Given: Given: - The actual volume of the rectangular prism (V_actual) = 80 cm³ - The measured dimensions of the prism are 4.53 cm by 2.02 cm by 7.69 cm. First, we need to calculate the volume using the measured dimensions. V_measured = length × width × heightCalculate volume: Calculate the measured volume: V_measured = 4.53 cm × 2.02 cm × 7.69 cm V_measured = 70.300034 cm³Calculate absolute error: Now, we find the absolute error, which is the difference between the actual volume and the measured volume. Absolute error = |V_actual - V_measured|Calculate relative error: Calculate the absolute error: Absolute error = |80 cm³ - 70.300034 cm³| Absolute error = 9.699966 cm³Round relative error: Next, we calculate the relative error, which is the absolute error divided by the actual volume. Relative error = Absolute error / V_actualCalculate the relative error: Relative error = 9.699966 cm³ / 80 cm³ Relative error = 0.121249575Finally, we round the relative error to the nearest hundredth. Relative error (rounded) = 0.12

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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

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) $= 0.12$