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Summary

In this video, the presenter explains how to calculate the area of a circle's cross-section, using two examples. The first example focuses on calculating the area of a sector with a 72-degree angle and a 20 cm radius, while the second example involves a 45-degree angle and a 28 cm radius. The presenter walks through the process step-by-step, explaining the formulas and calculations involved, including the choice of the constant value for Pi (3.14 or 22/7). The video provides clear and detailed instructions, making it easy for viewers to understand and apply the concept of sector area calculations.

Takeaways

• 😀 The video discusses how to calculate the area of a sector of a circle.
• 😀 The formula to calculate the area of a sector is: (Angle of Sector / 360°) * π * r².
• 😀 The value of π can be either 22/7 or 3.14, depending on the radius or diameter of the circle.
• 😀 22/7 is used when the radius or diameter is a multiple of 7.
• 😀 3.14 is used when the radius or diameter is not a multiple of 7.
• 😀 In the first example, the radius of the circle is 20 cm and the central angle is 72°, leading to an area of 251.2 cm².
• 😀 The division and multiplication steps are demonstrated clearly for both calculating the area and simplifying the formula.
• 😀 The second example uses a 45° angle and a radius of 28 cm, resulting in an area of 154 cm².
• 😀 Simplifying fractions (like 72/360) is important to make the calculations easier.
• 😀 The video encourages viewers to support the channel by liking, subscribing, and pressing the bell button for notifications.

Q & A

What is the main topic discussed in the video?

The main topic discussed in the video is how to calculate the area of a circle's cross-section (sector), with examples demonstrating the calculation process using specific formulas.

What is the formula to calculate the area of a sector of a circle?

The formula to calculate the area of a sector is: (angle of the sector / 360) * π * radius².

When do we use 22/7 as the value of π?

We use 22/7 as the value of π when the radius or diameter is a multiple of 7 (e.g., 7, 14, 21, 28, etc.).

When do we use 3.14 as the value of π?

We use 3.14 as the value of π when the radius or diameter is not a multiple of 7.

In the first example, how do we calculate the area of the sector with a 72° angle and a radius of 20 cm?

First, simplify the fraction (72/360) to 1/5. Then, apply the formula: (1/5) * 3.14 * 20 * 20, which gives 251.2 cm².

What is the process of simplifying the fraction (72/360)?

To simplify (72/360), divide both the numerator and denominator by their greatest common divisor, which is 72. This results in 72/360 being simplified to 1/5.

How do we handle decimal multiplication in the example with the radius of 20 cm?

To handle decimal multiplication, move the decimal point to eliminate it. For example, multiplying 3.14 by 20 * 20 results in 314, which can then be multiplied and simplified.

In the second example, what is the radius and angle given, and how is the area calculated?

In the second example, the radius is 28 cm, and the angle is 45°. The area is calculated using the formula: (45/360) * (22/7) * 28 * 28, which results in 154 cm².

What is the importance of simplifying the fraction (45/360) in the second example?

Simplifying (45/360) to 1/8 makes the calculation easier and more manageable by reducing the fraction before applying it to the formula.

Why is the result in cm² when calculating the area of a sector?

The result is in cm² because we are calculating an area, and the unit for area is always squared (e.g., cm²).