The volume of a rectangular prism is 480cm^(3). David measures the sides to be 6.49 cm by 9.99cm by 8.41cm. In calculating the volume, what is the relative error, to the nearest hundredth. Answer:

Calculate Volume: Calculate the volume of the rectangular prism using the measured sides. Volume = Length × Width × Height Volume = 6.49 cm × 9.99 cm × 8.41 cmPerform Multiplication: Perform the multiplication to find the calculated volume. Calculated Volume = 6.49 × 9.99 × 8.41 Calculated Volume ≈ 54.5809 × 8.41 Calculated Volume ≈ 458.903289 cm³Find Absolute Error: Find the absolute error by subtracting the given volume from the calculated volume. Absolute Error = |Calculated Volume - Given Volume| Absolute Error = |458.903289 cm³ - 480 cm³| Absolute Error ≈ | -21.096711 cm³| Absolute Error ≈ 21.10 cm³ (rounded to the nearest hundredth)Calculate Relative Error: Calculate the relative error by dividing the absolute error by the given volume and then converting it to a percentage. Relative Error = (Absolute Error / Given Volume) × 100% Relative Error = (21.10 cm³ / 480 cm³) × 100%Perform Division and Multiplication: Perform the division and multiplication to find the relative error percentage. Relative Error ≈ (0.0439583333) × 100% Relative Error ≈ 4.40% (rounded to the nearest hundredth)

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The volume of a rectangular prism is
480cm^(3). David measures the sides to be 6.49
cm by
9.99cm by
8.41cm. In calculating the volume, what is the relative error, to the nearest hundredth.
Answer:

The volume of a rectangular prism is $480 \mathrm{~cm}^{3}$ . David measures the sides to be $6$ . $49$ $\mathrm{cm}$ by $9.99 \mathrm{~cm}$ by $8.41 \mathrm{~cm}$ . In calculating the volume, what is the relative error, to the nearest hundredth. $\newline$ Answer:

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Q. The volume of a rectangular prism is

480 \mathrm{~cm}^{3}

. David measures the sides to be

6

49

\mathrm{cm}

9.99 \mathrm{~cm}

8.41 \mathrm{~cm}

. 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 measured sides. $\newline$ Volume = $\text{Length} \times \text{Width} \times \text{Height}$ $\newline$ Volume = $6.49\,\text{cm} \times 9.99\,\text{cm} \times 8.41\,\text{cm}$
Perform Multiplication: Perform the multiplication to find the calculated volume. $\newline$ Calculated Volume = $6.49 \times 9.99 \times 8.41$ $\newline$ Calculated Volume $\approx 54.5809 \times 8.41$ $\newline$ Calculated Volume $\approx 458.903289 \text{ cm}^3$
Find Absolute Error: Find the absolute error by subtracting the given volume from the calculated volume. $\newline$ Absolute Error = $|\text{Calculated Volume} - \text{Given Volume}|$ $\newline$ Absolute Error = $|458.903289 \text{ cm}^3 - 480 \text{ cm}^3|$ $\newline$ Absolute Error \approx $| -21.096711 \text{ cm}^3|$ $\newline$ Absolute Error \approx $21$ . $10$ \text{ cm}^ $3$ (rounded to the nearest hundredth)
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 = $(21.10 \, \text{cm}^3 / 480 \, \text{cm}^3) \times 100\%$
Perform Division and Multiplication: Perform the division and multiplication to find the relative error percentage. $\newline$ Relative Error $\approx (0.0439583333) \times 100\%$ $\newline$ Relative Error $\approx 4.40\%$ (rounded to the nearest hundredth)