Question

A flat rate shipping box is in the shape of a rectangular prism. You estimate that the volume of the box is 1050 cubic inches. You measure the box and find that it has a length of 14 inches, a width of 10 inches, and a height of 6.5 inches. Find the percent error. Round your answer to the nearest tenth of a percent.

Answer 1

15.4% (nearest tenth)

Explanation:

Estimated volume of the shipping box = 1050 in³

Actual volume of the shipping box using the given dimensions:

`\begin{aligned}\textsf{Volume of rectangular prism} & = \sf width * length * height\\\implies \textsf{Volume of shipping box} & = \sf 10 * 14 * 6.5\\& = \sf 910 \:\: in^3\end{aligned}`

Percent Error formula

`\textsf{Percent error}=\sf \left|(estimated\:value\:-actual\:value)/(actual\:value) \right| * 100\%`

Substitute the estimated and actual volumes into the formula and solve for percent error:

`\begin{aligned}\implies \textsf{Percent error} & =\sf \left|(1050-910)/(910) \right| * 100\% \\& =\sf \left|(2)/(13) \right| * 100\% \\& =\sf (2)/(13) * 100\% \\& =\sf 15.4\% \:\: (nearest\:tenth) \end{aligned}`

Answer 2

• 15.4% overestimate

Explanation:

Given:

• Estimated volume V = 1050 in³
• Dimensions l = 14 in, w = 10 in, h = 6.5 in

Find the volume:

• V = lwh = 14*10*6.5 = 910 in³

The error is:

• 1050 - 910 = 140

The percent error is:

• 140/910*100% = 15.4%