Chapter 2.10, Problem 30P

The measured dimensions of a shape or a solid are given to the nearest whole unit. Find the greatest percent error of each shape or solid.

The volume of a rectangular prism with length $22\text{cm},$ width $36\text{cm},$ and height $19\text{cm}$

To determine

To find the greatest percent error of each shape or solid.

Answer to Problem 30P

952

Explanation of Solution

Given:

Length of prism: 22 cm

Width of prism: 36 cm

Height of prism: 19 cm

Formula used:

Volume of rectangular prism $=l\times b\times h$

Calculation:

Considering the actual given dimensions and calculating the volume,

  $\begin{array}{c}V=22\times 36\times 19\\ =15,048\end{array}$

Given that the dimensions are to the nearest whole unit.

So, the dimensions to the nearest whole unit is,

Length: 20 cm

Width: 40 cm

Height: 20 cm

The volume rounded to the nearest whole unit is,

  $\begin{array}{c}{V}_0=20\times 40\times 20\\ =16,000\end{array}$

The greatest percentage error is the difference between the dimension to the nearest whole unit and the actual dimensions.

  $\begin{array}{c}{V}_0-V=16,000-15,048\\ =952\end{array}$

Conclusion:

The greatest percentage error is 952.