The volume of a rectangular prism is 168ft^(3). David measures the sides to be 6.84ft by 2.82ft by 8.11ft. In calculating the volume, what is the relative error, to the nearest thousandth. Answer:

Calculate Volume: Calculate the volume using the given measurements. We will multiply the length, width, and height to find the calculated volume of the rectangular prism. Calculated Volume = Length × Width × Height Calculated Volume = 6.84ft × 2.82ft × 8.11ftPerform Multiplication: Perform the multiplication to find the calculated volume. Calculated Volume = 6.84 × 2.82 × 8.11 Calculated Volume = 155.66568ft³Find Absolute Error: Find the absolute error by subtracting the actual volume from the calculated volume. Absolute Error = |Calculated Volume - Actual Volume| Absolute Error = |155.66568ft³ - 168ft³|Perform Subtraction: Perform the subtraction to find the absolute error. Absolute Error = |155.66568ft³ - 168ft³| Absolute Error = |-12.33432ft³| Absolute Error = 12.33432ft³ (since absolute value is always positive)Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual volume. Relative Error = Absolute Error / Actual Volume Relative Error = 12.33432ft³ / 168ft³Perform Division: Perform the division to find the relative error. Relative Error = 12.33432ft³ / 168ft³ Relative Error ≈ 0.07342 (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
168ft^(3). David measures the sides to be
6.84ft by
2.82ft by
8.11ft. In calculating the volume, what is the relative error, to the nearest thousandth.
Answer:

The volume of a rectangular prism is $168 \mathrm{ft}^{3}$ . David measures the sides to be $6.84 \mathrm{ft}$ by $2.82 \mathrm{ft}$ by $8.11 \mathrm{ft}$ . In calculating the volume, what is the relative error, to the nearest thousandth. $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Find probabilities using the binomial distribution

Full solution

Q. The volume of a rectangular prism is

168 \mathrm{ft}^{3}

. David measures the sides to be

6.84 \mathrm{ft}

2.82 \mathrm{ft}

8.11 \mathrm{ft}

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

\newline

Answer:

Calculate Volume: Calculate the volume using the given measurements. $\newline$ We will multiply the length, width, and height to find the calculated volume of the rectangular prism. $\newline$ Calculated Volume = Length $\times$ Width $\times$ Height $\newline$ Calculated Volume = $6.84\,\text{ft} \times 2.82\,\text{ft} \times 8.11\,\text{ft}$
Perform Multiplication: Perform the multiplication to find the calculated volume. $\newline$ Calculated Volume = $6.84 \times 2.82 \times 8.11$ $\newline$ Calculated Volume = $155.66568\text{ft}^3$
Find Absolute Error: Find the absolute error by subtracting the actual volume from the calculated volume. $\newline$ Absolute Error = $|\text{Calculated Volume} - \text{Actual Volume}|$ $\newline$ Absolute Error = $|155.66568\text{ft}³ - 168\text{ft}³|$
Perform Subtraction: Perform the subtraction to find the absolute error. $\newline$ Absolute Error = $|155.66568\text{ft}^3 - 168\text{ft}^3|$ $\newline$ Absolute Error = $|-12.33432\text{ft}^3|$ $\newline$ Absolute Error = $12.33432\text{ft}^3$ (since absolute value is always positive)
Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual volume. $\newline$ Relative Error = $\frac{\text{Absolute Error}}{\text{Actual Volume}}$ $\newline$ Relative Error = $\frac{12.33432\text{ft}^3}{168\text{ft}^3}$
Perform Division: Perform the division to find the relative error. $\newline$ Relative Error = $\frac{12.33432\text{ft}³}{168\text{ft}³}$ $\newline$ Relative Error $\approx 0.07342$ (to the nearest thousandth)