# Measure the area of the rectangular box with length of 11.5 cm (plus or minus) 0.1 cm, and a height of 1 cm(plus or minus) 0.1 cm. Use a two-repetition approach: the highest and lowest possible bounds. The standard or accepted value is 9.80 cm^2. Give the percent relative and absolute errors. Discuss the sources of these errors. Which dimension contributes greatest to the relative error?

Question
24 views

Measure the area of the rectangular box with length of 11.5 cm (plus or minus) 0.1 cm, and a height of 1 cm(plus or minus) 0.1 cm. Use a two-repetition approach: the highest and lowest possible bounds. The standard or accepted value is 9.80 cm^2. Give the percent relative and absolute errors. Discuss the sources of these errors. Which dimension contributes greatest to the relative error?

check_circle

star
star
star
star
star
1 Rating
Step 1

Introduction:

Absolute error = | Observed value – Expected value |.

Relative error = (Observed value – Expected value)/ Expected value.

Relative absolute error = | Observed value – Expected value |/ Expected value.

Percent relative error = (Observed value – Expected value)/ Expected value × 100%.

Step 2

Calculation:

Length:

The length is given as (11.5 ± 0.1) cm.

So, the absolute error for length is 0.1 cm.

Relative error percentage

= (0.1/11.5) × 100%

= 0.87%.

So, the percent relative absolute error for length is 0.87%.

Height:

The height is given as (1 ± 0.1) cm.

So, the absolute error for height is 0.1 cm.

Relative error percentage

= (0.1/1) × 100%

= 10%.

So, the percent relative absolute error for height is 10%.

Area:

Lowest possible bound of length = (11.5 – 0.1) cm = 11.4 cm.

Highest possible bound of length = (11.5 + 0.1) cm = 11.6 cm.

Lowest possible bound of height = (1 – 0.1) cm = 0.9 cm.

Highest possible bound of height = (1 + 0.1) cm = 1.1 cm.

Thus, lowest possible bound of area = (11.4 × 0.9) cm = 10.26 cm.

Highest possible bound of area = (11.6 × 1.1) cm = 12.76 cm.

The standard or expected value of area = 9.8 cm2.

With respect to the lowest possible bound of area, absolute error = (10.26 – 9.8) cm = 0.46 cm.

So, the absolute error for area with respect to the lowest possible bound of area is...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Probability 