The volume of a rectangular prism is 54ft^(3). Carter measures the sides to be 2.85ft by 9.32ft by 2.09ft. In calculating the volume, what is the relative error, to the nearest thousandth. Answer:

Given: Given: Actual volume (V_actual) = 54ft³ Measured sides are 2.85ft, 9.32ft, and 2.09ft. To find the calculated volume (V_calculated), we multiply the measured sides: V_calculated = 2.85ft * 9.32ft * 2.09ftPerform multiplication: Perform the multiplication to find the calculated volume: V_calculated = 2.85 * 9.32 * 2.09 V_calculated = 55.59666ft³ (rounded to five decimal places for intermediate calculation)Calculate relative error: The relative error is calculated using the formula: Relative Error = |V_actual - V_calculated| / V_actual First, find the absolute difference between the actual volume and the calculated volume: Difference = |V_actual - V_calculated| Difference = |54 - 55.59666| Difference = 1.59666ft³ (rounded to five decimal places for intermediate calculation)Find absolute difference: Now, calculate the relative error using the difference found: Relative Error = Difference / V_actual Relative Error = 1.59666 / 54 Relative Error ≈ 0.029568 (rounded to six decimal places for intermediate calculation)Calculate relative error: Round the relative error to the nearest thousandth as requested: Relative Error ≈ 0.030 (to the nearest thousandth)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The volume of a rectangular prism is
54ft^(3). Carter measures the sides to be
2.85ft by
9.32ft by
2.09ft. In calculating the volume, what is the relative error, to the nearest thousandth.
Answer:

The volume of a rectangular prism is $54 \mathrm{ft}^{3}$ . Carter measures the sides to be $2.85 \mathrm{ft}$ by $9.32 \mathrm{ft}$ by $2.09 \mathrm{ft}$ . In calculating the volume, what is the relative error, to the nearest thousandth. $\newline$ Answer:

View step-by-step help

Home

Math Problems

Calculus

Find the rate of change of one variable when rate of change of other variable is given

Full solution

Q. The volume of a rectangular prism is

54 \mathrm{ft}^{3}

. Carter measures the sides to be

2.85 \mathrm{ft}

9.32 \mathrm{ft}

2.09 \mathrm{ft}

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

\newline

Answer:

Given: Given: $\newline$ Actual volume $V_{\text{actual}}$ = $54\,\text{ft}^3$ $\newline$ Measured sides are $2.85\,\text{ft}$ , $9.32\,\text{ft}$ , and $2.09\,\text{ft}$ . $\newline$ To find the calculated volume $V_{\text{calculated}}$ , we multiply the measured sides: $\newline$ $V_{\text{calculated}} = 2.85\,\text{ft} \times 9.32\,\text{ft} \times 2.09\,\text{ft}$
Perform multiplication: Perform the multiplication to find the calculated volume: $\newline$ $V_{\text{calculated}} = 2.85 \times 9.32 \times 2.09$ $\newline$ $V_{\text{calculated}} = 55.59666\text{ft}^3$ (rounded to five decimal places for intermediate calculation)
Calculate relative error: The relative error is calculated using the formula: $\newline$ Relative Error = $\left| V_{\text{actual}} - V_{\text{calculated}} \right| / V_{\text{actual}}$ $\newline$ First, find the absolute difference between the actual volume and the calculated volume: $\newline$ Difference = $\left| V_{\text{actual}} - V_{\text{calculated}} \right|$ $\newline$ Difference = $\left| 54 - 55.59666 \right|$ $\newline$ Difference = $1.59666$ ft³ (rounded to five decimal places for intermediate calculation)
Find absolute difference: Now, calculate the relative error using the difference found: $\newline$ Relative Error = $\frac{\text{Difference}}{V_{\text{actual}}}$ $\newline$ Relative Error = $\frac{1.59666}{54}$ $\newline$ Relative Error $\approx 0.029568$ (rounded to six decimal places for intermediate calculation)
Calculate relative error: Round the relative error to the nearest thousandth as requested: $\newline$ Relative Error $\approx 0.030$ (to the nearest thousandth)