IXL - Minimum and maximum area and volume (Geometry practice)

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

3 m

11 m

18 m

If necessary, round your answers to the nearest thousandth.

Minimum possible volume = m³

Maximum possible volume = m³

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question

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

1 yd

3 yd

11 yd

If necessary, round your answers to the nearest thousandth.

Minimum possible volume = yd³

Maximum possible volume = yd³

key idea

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.

solution

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 yard, so the greatest possible error is half of 1 yard, which is 0.5 yards.

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

V_max

L_maxW_maxH_max

Add
the
greatest
possible
error,
0.5

(1 + 0.5)(3 + 0.5)(11 + 0.5)

Add
the
greatest
possible
error,
0.5

(1.5)(3.5)(11.5)

60.375

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

V_min

L_minW_minH_min

Subtract
the
greatest
possible
error,
0.5

(1 − 0.5)(3 − 0.5)(11 − 0.5)

Subtract
the
greatest
possible
error,
0.5

(0.5)(2.5)(10.5)

13.125

The
minimum
possible
volume
is
13.125
cubic
yards,
and
the
maximum
possible
volume
is
60.375
cubic
yards.

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Not feeling ready yet? These can help:

V.5Greatest possible error

HH.1Volume of cubes and rectangular prisms

S.2Area of rectangles and squares

D.3Multiply decimals

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