example
A circular sandbox has a radius of
2.5 feet. Find 1. the circumference and 2. the area of the sandbox.
Solution
1.
Step 1. Read the problem. Draw the figure and label it with the given information. |
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Step 2. Identify what you are looking for. |
The circumference of the circle |
Step 3. Name. Choose a variable to represent it. |
Let c = circumference of the circle |
Step 4. Translate.
Write the appropriate formula
Substitute |
C=2πr
C=2π(2.5) |
Step 5. Solve the equation. |
C≈2(3.14)(2.5)
C≈15ft |
Step 6. Check. Does this answer make sense?
Yes. If we draw a square around the circle, its sides would be 5 ft (twice the radius), so its perimeter would be 20 ft. This is slightly more than the circle's circumference, 15.7 ft.
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|
Step 7. Answer the question. |
The circumference of the sandbox is 15.7 feet. |
2.
Step 1. Read the problem. Draw the figure and label it with the given information. |
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Step 2. Identify what you are looking for. |
The area of the circle |
Step 3. Name. Choose a variable to represent it. |
Let A = the area of the circle |
Step 4. Translate.
Write the appropriate formula
Substitute |
A=πr2
A=π(2.5)2 |
Step 5. Solve the equation. |
A≈(3.14)(2.5)2
A≈19.625sq. ft |
Step 6. Check.
Yes. If we draw a square around the circle, its sides would be 5 ft, as shown in part ⓐ. So the area of the square would be 25 sq. ft. This is slightly more than the circle's area, 19.625 sq. ft. |
|
Step 7. Answer the question. |
The area of the circle is 19.625 square feet. |
example
A circular table has a diameter of four feet. What is the circumference of the table?
Answer:
Solution
Step 1. Read the problem. Draw the figure and label it with the given information. |
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Step 2. Identify what you are looking for. |
The circumference of the table |
Step 3. Name. Choose a variable to represent it. |
Let C = the circumference of the table |
Step 4. Translate.
Write the appropriate formula for the situation.
Substitute. |
C=πd
C=π(4) |
Step 5. Solve the equation, using 3.14 for π. |
C≈(3.14)(4)
C≈12.56feet |
Step 6. Check: If we put a square around the circle, its side would be 4.
The perimeter would be 16. It makes sense that the circumference of the circle, 12.56, is a little less than 16.
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Step 7. Answer the question. |
The diameter of the table is 12.56 square feet. |
example
Find the diameter of a circle with a circumference of
47.1 centimeters.
Answer:
Solution
Step 1. Read the problem. Draw the figure and label it with the given information. |
C=47.1cm |
Step 2. Identify what you are looking for. |
The diameter of the circle |
Step 3. Name. Choose a variable to represent it. |
Let d = the diameter of the circle |
Step 4. Translate. |
|
Write the formula.
Substitute, using 3.14 to approximate π . |
C=πd
47.1≈3.14d |
Step 5. Solve. |
3.1447.1≈3.143.14d
15≈d |
Step 6. Check:
C=πd
47.1=?(3.14)(15)
47.1=47.1✓ |
|
Step 7. Answer the question. |
The diameter of the circle is approximately 15 centimeters. |
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