Minimum and maximum area and volume

key notes :

🎯 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.

Learn with an example

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

Minimum possible volume = ________ cm³

Maximum possible volume = _______ cm³

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 centimetre, so the greatest possible error is half of 1 centimetre, which is 0.5 centimetres.

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

Vmax = LmaxWmaxHmax

= (11 + 0.5)(20 + 0.5)(8 + 0.5) Add the greatest possible error, 0.5

= (11.5)(20.5)(8.5)

= 2,003.875

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

Vmin
 = 
LminWminHmin

= (11 − 0.5)(20 − 0.5)(8 − 0.5) Subtract the greatest possible error, 0.5

= (10.5)(19.5)(7.5)

= 1,535.625

The minimum possible volume is 1,535.625 cubic centimetres, and the maximum possible volume is 2,003.875 cubic centimetres.

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

Minimum possible volume = ________ m³

Maximum possible volume = ________ m³

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 metre, so the greatest possible error is half of 1 metre, which is 0.5 metres.

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

Vmax = LmaxWmaxHmax

= (7 + 0.5)(12 + 0.5)(18 + 0.5) Add the greatest possible error, 0.5

= (7.5)(12.5)(18.5)

= 1,734.375

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

Vmin = LminWminHmin

= (7 − 0.5)(12 − 0.5)(18 − 0.5) Subtract the greatest possible error, 0.5

= (6.5)(11.5)(17.5)

= 1,308.125

The minimum possible volume is 1,308.125 cubic metres, and the maximum possible volume is 1,734.375 cubic metres.

The rectangle below is labelled with its measured dimensions. Taking measurement error into account, what are the minimum and maximum possible areas?

Minimum possible area = ________ km²

Maximum possible area = ________ km²

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

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

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

Amax = LmaxWmax

= (2 + 0.5)(9 + 0.5) Add the greatest possible error, 0.5

= (2.5)(9.5)

= 23.75

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

Amin = LminWmin

= (2 − 0.5)(9 − 0.5) Subtract the greatest possible error, 0

= (1.5)(8.5)

= 12.75

The minimum possible area is 12.75 square kilometres, and the maximum possible area is 23.75 square kilometres.

Let’s practice!🖊️