Understanding Pi: Exploration and Applications
Explore the fundamental constant Pi (π), its definition, properties, and practical applications in geometry and real-world scenarios for Grade 11 students.
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Understanding Pi: Exploration and Applications
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Read each question carefully and answer to the best of your ability. Show all your work for calculations.
1. What is the definition of Pi (π)?
The ratio of a circle's area to its radius squared.
The ratio of a circle's circumference to its diameter.
The ratio of a circle's diameter to its circumference.
The ratio of a circle's circumference to its radius.
2. Which of the following best describes Pi?
A rational number.
An imaginary number.
An irrational number.
An integer.
3. The formula for the circumference of a circle is C = .
4. The formula for the area of a circle is A = .
5. Pi is a mathematical constant that is approximately equal to .
6. A circular garden has a diameter of 10 meters. Calculate its circumference and area. Use π ≈ 3.14.
7. Explain how Pi is used in calculating the volume of a cylinder. Draw a simple diagram to illustrate your explanation.
8. Pi is a repeating decimal that eventually terminates.
True
False
9. The value of Pi changes depending on the size of the circle.
True
False
Match each term with its correct definition or formula.
10. Circumference
a. πr²
11. Area of a circle
b. The distance around a circle
12. Diameter
c. 2πr
13. Radius
d. A line segment passing through the center of a circle, connecting two points on the circumference
14. Volume of a cylinder
e. A line segment from the center of a circle to any point on its circumference