The volume of a rectangular prism is 108cm^(3). Eric measures the sides to be 3.32cm by 4.04cm by 8.72cm. In calculating the volume, what is the relative error, to the nearest thousandth. Answer:

Calculate Volume: Calculate the volume of the rectangular prism using the measurements provided by Eric. Volume = length × width × height Volume = 3.32 cm × 4.04 cm × 8.72 cmPerform Multiplication: Perform the multiplication to find the calculated volume. Calculated Volume = 3.32 × 4.04 × 8.72 Calculated Volume = 116.905728 cm³Compare Volumes: Compare the calculated volume with the actual volume to find the absolute error. Absolute Error = |Actual Volume - Calculated Volume| Absolute Error = |108 cm³ - 116.905728 cm³| Absolute Error = | -8.905728 cm³ | Absolute Error = 8.905728 cm³Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual volume and then converting it to a percentage. Relative Error = (Absolute Error / Actual Volume) × 100% Relative Error = (8.905728 cm³ / 108 cm³) × 100%Perform Division and Multiplication: Perform the division and multiplication to find the relative error as a percentage. Relative Error = (8.905728 / 108) × 100% Relative Error = 0.082462% (rounded 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
108cm^(3). Eric measures the sides to be
3.32cm by
4.04cm by
8.72cm. In calculating the volume, what is the relative error, to the nearest thousandth.
Answer:

The volume of a rectangular prism is $108 \mathrm{~cm}^{3}$ . Eric measures the sides to be $3.32 \mathrm{~cm}$ by $4.04 \mathrm{~cm}$ by $8.72 \mathrm{~cm}$ . In calculating the volume, what is the relative error, to the nearest thousandth. $\newline$ Answer:

View step-by-step help

Home

Math Problems

Grade 8

Circles: word problems

Full solution

Q. The volume of a rectangular prism is

108 \mathrm{~cm}^{3}

. Eric measures the sides to be

3.32 \mathrm{~cm}

4.04 \mathrm{~cm}

8.72 \mathrm{~cm}

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

\newline

Answer:

Calculate Volume: Calculate the volume of the rectangular prism using the measurements provided by Eric. $\newline$ Volume = length $\times$ width $\times$ height $\newline$ Volume = $3.32\, \text{cm}$ $\times$ $4.04\, \text{cm}$ $\times$ $8.72\, \text{cm}$
Perform Multiplication: Perform the multiplication to find the calculated volume. $\newline$ Calculated Volume = $3.32 \times 4.04 \times 8.72$ $\newline$ Calculated Volume = $116.905728 \, \text{cm}^3$
Compare Volumes: Compare the calculated volume with the actual volume to find the absolute error. $\newline$ Absolute Error = $|\text{Actual Volume} - \text{Calculated Volume}|$ $\newline$ Absolute Error = $|108 \text{ cm}^3 - 116.905728 \text{ cm}^3|$ $\newline$ Absolute Error = $| -8.905728 \text{ cm}^3 |$ $\newline$ Absolute Error = $8$ . $905728$ \text{ cm}^ $3$
Calculate Relative Error: Calculate the relative error by dividing the absolute error by the actual volume and then converting it to a percentage. $\newline$ Relative Error = $(\text{Absolute Error} / \text{Actual Volume}) \times 100\%$ $\newline$ Relative Error = $(8.905728 \, \text{cm}^3 / 108 \, \text{cm}^3) \times 100\%$
Perform Division and Multiplication: Perform the division and multiplication to find the relative error as a percentage. $\newline$ Relative Error = $(8.905728 / 108) \times 100\%$ $\newline$ Relative Error = $0.082462\%$ (rounded to the nearest thousandth)