IXL - Percent error: area and volume (Algebra 1 practice)

The rectangle below is labeled with its measured dimensions. Taking measurement error into account, what is the percent error in its calculated area?

16 ft

3 ft

Round your answer to the nearest tenth of a percent and include a percent sign (%).

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question

The rectangular prism below is labeled with its measured dimensions. Taking measurement error into account, what is the percent error in its calculated volume?

9 m

4 m

8 m

Round your answer to the nearest tenth of a percent and include a percent sign (%).

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 percent error in volume, taking measurement error into account.

Step 1: Find the measured volume.

To find the measured volume, multiply the measured dimensions.

V_meas

L_measW_measH_meas

(9)(8)(4)

288

Step 2: Find the minimum possible volume and the maximum possible volume.

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

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

(9 + 0.5)(8 + 0.5)(4 + 0.5)

Add
the
greatest
possible
error,
0.5

(9.5)(8.5)(4.5)

363.375

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

(9 − 0.5)(8 − 0.5)(4 − 0.5)

Subtract
the
greatest
possible
error,
0.5

(8.5)(7.5)(3.5)

223.125

Step 3: Find the greater difference in volume.

Calculate the difference between the minimum volume and the measured volume, and between the maximum volume and the measured volume. The larger difference will be the greatest possible error in volume.

Difference using minimum volume:

V_meas

−

V_min

288

−

223.125

64.875

Difference using maximum volume:

V_max

−

V_meas

363.375

−

288

75.375

The
second
difference
is
larger.
So,
the
greatest
possible
error
in
volume
is
75.375
.

Step 4: Calculate the percent error in the volume.

percent error in volume

greatest possible error in volume

measured volume

75.375

288

≈

0.26172

Write the number as a percent.

0.26172 → 26.172%

Round to the nearest tenth of a percent.

26.172% → 26.2%

To the nearest tenth of a percent, the percent error is 26.2%.

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D.6Minimum and maximum area and volume

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