Year 11 Maths: Percent Error: Area and Volume

Understanding Percent Error

What is Percent Error?

Percent error helps us understand how accurate our measurements are. It shows the difference between a measured value and a true or accepted value compared to the true value. We often use it in science and maths to see how close our calculations are to the real thing.

How to Calculate Percent Error

To calculate percent error, we use the following formula:

Let’s Break It Down

1. Measured Value: This is what you got from your calculation or measurement.
2. True Value: This is the correct or accepted value.
3. Absolute Difference: This means we only care about how far off we are, not whether we are over or under. That’s why we use the absolute value (the positive version).
4. Divide by True Value: This tells us how big the error is compared to what we expected.
5. Multiply by 100: This converts our fraction into a percentage.

Example 1: Area

Imagine you measured the area of a rectangle and got 50 cm², but the true area is 60 cm².

1. Measured Value = 50 cm²
2. True Value = 60 cm²
3. Calculate the Difference:
   • Difference = |50 – 60| = 10
4. Divide by True Value:
   • $$\frac{10}{60} = \frac{1}{6} \approx 0.1667$$
5. Convert to Percentage:
   • $$0.1667 \times 100 \approx 16.67%$$

So, the percent error in the area is approximately 16.67%.

Example 2: Volume

Now, let’s say you measured the volume of a box and got 120 cm³, but the actual volume is 150 cm³.

1. Measured Value = 120 cm³
2. True Value = 150 cm³
3. Calculate the Difference:
   • Difference = |120 – 150| = 30
4. Divide by True Value:
   • $$\frac{30}{150} = \frac{1}{5} = 0.2$$
5. Convert to Percentage:
   • $$0.2 \times 100 = 20%$$

So, the percent error in the volume is 20%.

Key Rules to Remember

1. Always use absolute values for the difference.
2. Be careful to use the correct true value.
3. Make sure to multiply by 100 to get a percentage.

Tips and Tricks

• Double-check your measurements to ensure accuracy.
• Use a calculator for more complex calculations.
• Practice with different shapes and sizes for area and volume.

Practice Questions

Easy Level

1. Measured area: 30 cm²; True area: 35 cm². What is the percent error?
2. Measured volume: 80 cm³; True volume: 100 cm³. What is the percent error?
3. Measured area: 45 cm²; True area: 50 cm². What is the percent error?
4. Measured volume: 200 cm³; True volume: 250 cm³. What is the percent error?
5. Measured area: 60 cm²; True area: 70 cm². What is the percent error?
6. Measured volume: 140 cm³; True volume: 150 cm³. What is the percent error?
7. Measured area: 20 cm²; True area: 25 cm². What is the percent error?
8. Measured volume: 300 cm³; True volume: 350 cm³. What is the percent error?
9. Measured area: 90 cm²; True area: 100 cm². What is the percent error?
10. Measured volume: 50 cm³; True volume: 60 cm³. What is the percent error?
11. Measured area: 10 cm²; True area: 15 cm². What is the percent error?
12. Measured volume: 400 cm³; True volume: 500 cm³. What is the percent error?
13. Measured area: 25 cm²; True area: 30 cm². What is the percent error?
14. Measured volume: 600 cm³; True volume: 750 cm³. What is the percent error?
15. Measured area: 80 cm²; True area: 100 cm². What is the percent error?
16. Measured volume: 700 cm³; True volume: 800 cm³. What is the percent error?
17. Measured area: 55 cm²; True area: 60 cm². What is the percent error?
18. Measured volume: 250 cm³; True volume: 300 cm³. What is the percent error?
19. Measured area: 15 cm²; True area: 20 cm². What is the percent error?
20. Measured volume: 90 cm³; True volume: 100 cm³. What is the percent error?

Medium Level

1. Measured area: 125 cm²; True area: 150 cm². What is the percent error?
2. Measured volume: 350 cm³; True volume: 400 cm³. What is the percent error?
3. Measured area: 200 cm²; True area: 250 cm². What is the percent error?
4. Measured volume: 450 cm³; True volume: 500 cm³. What is the percent error?
5. Measured area: 75 cm²; True area: 100 cm². What is the percent error?
6. Measured volume: 250 cm³; True volume: 300 cm³. What is the percent error?
7. Measured area: 90 cm²; True area: 120 cm². What is the percent error?
8. Measured volume: 500 cm³; True volume: 600 cm³. What is the percent error?
9. Measured area: 65 cm²; True area: 80 cm². What is the percent error?
10. Measured volume: 150 cm³; True volume: 180 cm³. What is the percent error?
11. Measured area: 140 cm²; True area: 160 cm². What is the percent error?
12. Measured volume: 350 cm³; True volume: 400 cm³. What is the percent error?
13. Measured area: 33 cm²; True area: 48 cm². What is the percent error?
14. Measured volume: 280 cm³; True volume: 320 cm³. What is the percent error?
15. Measured area: 85 cm²; True area: 100 cm². What is the percent error?
16. Measured volume: 600 cm³; True volume: 750 cm³. What is the percent error?
17. Measured area: 110 cm²; True area: 150 cm². What is the percent error?
18. Measured volume: 500 cm³; True volume: 550 cm³. What is the percent error?
19. Measured area: 95 cm²; True area: 125 cm². What is the percent error?
20. Measured volume: 430 cm³; True volume: 470 cm³. What is the percent error?

Hard Level

1. Measured area: 375 cm²; True area: 400 cm². What is the percent error?
2. Measured volume: 850 cm³; True volume: 900 cm³. What is the percent error?
3. Measured area: 225 cm²; True area: 250 cm². What is the percent error?
4. Measured volume: 750 cm³; True volume: 800 cm³. What is the percent error?
5. Measured area: 140 cm²; True area: 160 cm². What is the percent error?
6. Measured volume: 920 cm³; True volume: 1000 cm³. What is the percent error?
7. Measured area: 85 cm²; True area: 90 cm². What is the percent error?
8. Measured volume: 600 cm³; True volume: 650 cm³. What is the percent error?
9. Measured area: 110 cm²; True area: 130 cm². What is the percent error?
10. Measured volume: 210 cm³; True volume: 250 cm³. What is the percent error?
11. Measured area: 300 cm²; True area: 350 cm². What is the percent error?
12. Measured volume: 500 cm³; True volume: 600 cm³. What is the percent error?
13. Measured area: 450 cm²; True area: 500 cm². What is the percent error?
14. Measured volume: 780 cm³; True volume: 800 cm³. What is the percent error?
15. Measured area: 290 cm²; True area: 300 cm². What is the percent error?
16. Measured volume: 700 cm³; True volume: 750 cm³. What is the percent error?
17. Measured area: 180 cm²; True area: 200 cm². What is the percent error?
18. Measured volume: 450 cm³; True volume: 500 cm³. What is the percent error?
19. Measured area: 400 cm²; True area: 450 cm². What is the percent error?
20. Measured volume: 960 cm³; True volume: 1000 cm³. What is the percent error?

Answers

Easy Level Answers

1. 14.29%
2. 20%
3. 10%
4. 12%
5. 14.29%
6. 20%
7. 20%
8. 14.29%
9. 10%
10. 16.67%
11. 33.33%
12. 20%
13. 16.67%
14. 20%
15. 20%
16. 20%
17. 8.33%
18. 16.67%
19. 25%
20. 10%

Medium Level Answers

1. 16.67%
2. 12.5%
3. 20%
4. 10%
5. 25%
6. 16.67%
7. 25%
8. 16.67%
9. 31.25%
10. 16.67%
11. 12.5%
12. 12.5%
13. 31.25%
14. 12.5%
15. 15%
16. 20%
17. 26.67%
18. 9.09%
19. 24%
20. 8.51%

Hard Level Answers

1. 6.67%
2. 5.56%
3. 10%
4. 6.25%
5. 12.5%
6. 8%
7. 5.88%
8. 7.69%
9. 15.38%
10. 16%
11. 14.29%
12. 16.67%
13. 10%
14. 2.5%
15. 3.45%
16. 6.67%
17. 10%
18. 10%
19. 11.11%
20. 4%

This lesson has covered how to understand and calculate percent error in areas and volumes. Feel free to review the concepts and practice the questions to enhance your understanding!