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Minimum and maximum volume

The rectangular prism below is labeled with its measured dimensions. Taking measurement error into account, what are the minimum and maximum possible volumes?

• To find the minimum possible volume, subtract the greatest possible error from each measurement before calculating.
• To find the maximum possible volume, add the greatest possible error to each measurement before calculating.

You want to find the minimum and maximum volume, taking measurement error into account.

First find the greatest possible error. Each measurement was made to the nearest whole inch, so the greatest possible error is half of 1 inch, which is 0.5 inches.

To find the maximum possible volume, add the greatest possible error to each measurement, then multiply.

 Vmax = LmaxWmaxHmax = (17 + 0.5)(9 + 0.5)(19 + 0.5) Add the greatest possible error, 0.5 = (17.5)(9.5)(19.5) = 3,241.875

To find the minimum possible volume, subtract the greatest possible error from each measurement, then multiply.

 Vmin = LminWminHmin = (17 – 0.5)(9 – 0.5)(19 – 0.5) Subtract the greatest possible error, 0.5 = (16.5)(8.5)(18.5) = 2,594.625

The minimum possible volume is 2,594.625 cubic inches, and the maximum possible volume is 3,241.875 cubic inches.

The rectangular prism below is labeled with its measured dimensions. Taking measurement error into account, what are the minimum and maximum possible volumes?

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The maximum possible volume is

The minimum possible volume is