MENGHITUNG PANJANG BUSUR

Summary

This educational video focuses on calculating the arc length of a circle, explaining key concepts such as the central angle, arc, and circumference. The speaker outlines the formula for finding the arc length by using the central angle and the total circumference, providing clear examples with step-by-step solutions. It includes problems such as calculating arc lengths for different angles, emphasizing the importance of understanding the relationship between the central angle and the circle’s circumference. The video encourages viewers to practice and apply the formula to improve their skills.

Takeaways

• 😀 Busur is the curved line that connects two points on a circle, forming a segment of the circle's circumference.
• 😀 The central angle, such as ∠AOB, is used to calculate the length of the arc between two points on the circle.
• 😀 The formula for the length of the arc is: length of arc AB = (∠AOB / 360°) * circumference of the circle.
• 😀 The central angle ∠AOB and the full circle's 360° are proportional to the length of the arc and the total circumference.
• 😀 The formula can be adapted based on the specific points involved in the arc, such as AB or CD.
• 😀 To calculate the length of an arc, the central angle and the circumference of the circle must be known.
• 😀 In the first example, with a right-angle (90°), the length of arc AB is calculated to be 11 cm, using the formula and the given circumference of 44 cm.
• 😀 For the second example, the formula is applied to find the length of the arc CD, with a central angle of 120° and a circle radius of 21 cm.
• 😀 The circumference of the circle is calculated using the formula 2 * π * r, with π approximated as 22/7, and the radius provided as 21 cm.
• 😀 The second example shows that the arc length is found by multiplying the fraction (120° / 360°) by the total circumference of the circle, resulting in a length of 44 cm.

Q & A

What is the definition of an arc in a circle?

An arc is the curved line segment on the circumference of a circle that connects two points on the circle.

What is the formula to calculate the length of an arc?

The formula to calculate the length of an arc is: Panjang Busur AB = (Sudut AOB / 360°) * Keliling Lingkaran.

What does Sudut AOB represent in the arc length formula?

Sudut AOB represents the central angle (in degrees) between two points on the circle, from the center of the circle.

How is the circumference of a circle calculated?

The circumference of a circle is calculated using the formula: Keliling = 2 * π * r, where r is the radius of the circle.

In the first example, what is the central angle for calculating the arc length?

In the first example, the central angle is 90°.

What is the circumference of the circle in the first example?

The circumference of the circle in the first example is 44 cm.

How do you calculate the length of an arc when the central angle is 90° and the circumference is 44 cm?

To calculate the length of the arc, use the formula: Panjang Busur AB = (90° / 360°) * 44 cm = 11 cm.

In the second example, what is the central angle and radius of the circle?

In the second example, the central angle is 120° and the radius of the circle is 21 cm.

How do you calculate the circumference in the second example when the radius is 21 cm?

The circumference is calculated as: Keliling = 2 * π * 21 cm = 132 cm (using π = 22/7).

What is the length of the arc in the second example when the central angle is 120° and the circumference is 132 cm?

The length of the arc is calculated as: Panjang Busur CD = (120° / 360°) * 132 cm = 44 cm.