Exploring Pi (π)
A Grade 12 math worksheet focusing on the properties, applications, and calculations involving the mathematical constant Pi (π) in geometry and advanced contexts.
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Exploring Pi (π)
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Read each question carefully and answer to the best of your ability. Show all your work for calculations.
1. Which of the following best defines 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 area of a circle with a radius of 1.
2. A circular garden has a circumference of 31.4 meters. What is the approximate radius of the garden? (Use π ≈ 3.14)
2.5 meters
5 meters
10 meters
15.7 meters
3. Pi (π) is an number, meaning its decimal representation is non-terminating and non-repeating.
4. The formula for the area of a circle with radius 'r' is A = .
5. A sector of a circle has a radius of 8 cm and a central angle of 45 degrees. Calculate the arc length and the area of the sector. Express your answer in terms of π.
6. Pi (π) is a rational number because it can be expressed as a fraction (22/7).
True
False
7. The volume of a cylinder is calculated using the formula V = πr²h.
True
False
8. A cylindrical water tank has a height of 10 meters and a base radius of 3 meters. Calculate the volume of water the tank can hold. Use π ≈ 3.14 and round your answer to two decimal places.
Match each term with its correct definition or formula.
9. Circumference
a. The distance around a circle.
10. Area of a circle
b. πr²
11. Diameter
c. 2r