Q8 Compare the areas of the red and... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 1: Q8 (page 4)

Compare the areas of the red and blue regions. (Area of circle = .)

Short Answer

Expert verified

The red and blue region of the circle represents that their areas are equal to each other but not exactly.

Step by step solution

Step 1. Determine the radius of the red region

Use a ruler to determine the diameter of the red region which is 11 cm. The half of the diameter represents the radius of a circle so the radius of the red region is .

Step 2. Determine the area of red region

Use the formula of the area of a circle and substitute in it after it performs the simplification.

Step 3. Determine the radius of the whole circle

Use a ruler to determine the diameter of the whole circle which is cm. The half of the diameter represents the radius of a circle so the radius of the whole circle is .

Step 4. Determine the area of whole circle

Use the formula of the area of a circle and substitute in it after it performs the simplification.

Step 5. Determine the radius of the inner circle

Use a ruler to determine the diameter of the inner circle which is 15 cm. The half of the diameter represents the radius of a circle so the radius of the inner circle is .

Step 6. Determine the area of inner circle

Use the formula of the area of a circle and substitute in it after it performs the simplification.

Step 7. Determine the area of blue region

To determine the area of the blue region performs the subtraction of the area of the inner circle from the area of the outer circle.

Step 8. Compare the area of both the regions and make conclusion

The area of the red region is and the area of the blue region is . This shows that the areas of both the regions are equal to each other but not exactly.