Circles - Area, Circumference, Radius & Diameter Explained!

Summary

In this video, viewers learn how to calculate the area and circumference of a circle using essential formulas and examples. It covers key concepts like radius, diameter, and the constant pi, explaining how to derive the radius from the diameter and vice versa. The video walks through several problems, illustrating how to find area from radius and circumference, as well as how to calculate circumference using diameter and area. By the end, viewers gain a clear understanding of these mathematical principles, enhancing their ability to solve related problems confidently.

Takeaways

• 😀 The radius of a circle is the distance from the center to any point on the circle.
• 😀 The diameter is twice the radius, represented as d = 2r.
• 😀 The area of a circle can be calculated using the formula A = πr².
• 😀 The circumference of a circle is the distance around it, calculated as C = 2πr.
• 😀 The approximate value of π used in calculations is typically 3.14.
• 😀 When given the radius, you can find the area and circumference using their respective formulas.
• 😀 The area unit is always in square units (e.g., square feet), while circumference uses linear units (e.g., feet).
• 😀 If given the diameter, you can find the radius by dividing the diameter by 2.
• 😀 To find the radius from a known area, rearrange the area formula: r = √(A/π).
• 😀 When given the circumference, you can derive the radius and subsequently the diameter using the circumference formula.

Q & A

What are the definitions of the radius and diameter of a circle?

The radius is the distance from the center of the circle to any point on the circle, while the diameter is twice the length of the radius, spanning from one edge of the circle through the center to the opposite edge.

What formulas are used to calculate the area and circumference of a circle?

The area of a circle is calculated using the formula A = πr², and the circumference is calculated using the formula C = 2πr.

What is the approximate value of π commonly used in calculations?

The approximate value of π commonly used in calculations is 3.14.

How do you calculate the area of a circle given its radius?

To calculate the area, you square the radius and multiply by π. For example, if the radius is 5 feet, the area would be A = π(5²) = 25π square feet, which is approximately 78.5 square feet using π ≈ 3.14.

If the diameter of a circle is given, how can you find the radius?

To find the radius from the diameter, divide the diameter by 2. For example, if the diameter is 14 inches, the radius would be 14/2 = 7 inches.

How can you calculate the circumference if you only know the area of the circle?

First, use the area formula A = πr² to solve for r, then use the circumference formula C = 2πr. For example, if the area is 100 square yards, first find r, then use it to find C.

What unit of measurement is used for area, and how does it differ from the unit for radius or circumference?

Area is measured in square units (e.g., square feet, square inches), while radius and circumference are measured in linear units (e.g., feet, inches).

In the example where the circumference is given as 14.5 feet, how do you find the radius?

You use the circumference formula C = 2πr. Plugging in C = 14.5 feet and using π ≈ 3.14, you would solve for r, leading to a radius of approximately 2.31 feet.

What is the area of a circle if the circumference is given as 18π meters?

First, find the radius using the circumference formula: C = 2πr. Setting C = 18π gives r = 9 meters. Then, use A = πr² to find the area: A = 81π square meters, approximately 254 square meters using π ≈ 3.14.

How do you round answers in the calculations of the area and circumference?

Answers are typically rounded to a specific number of significant figures or decimal places. For example, if the calculated area is 153.86 square inches, it may be rounded to 154 square inches.