Lingkaran (Bagian 2) - Keliling Lingkaran | Soal dan Pembahasan Matematika SMP MTs

Summary

This educational video script focuses on teaching the circumference and area of circles. It introduces formulas for calculating circumference (C = 2πr or C = πd) and area (A = πr²), using π values of 22/7 or 3.14. The script guides through examples, including finding circumference and radius from given diameters or circumferences, and solving practical problems involving half-circles and quarter-circles in geometric shapes. It concludes with a teaser for the next video, which will cover the area of circles.

Takeaways

• 📘 The video focuses on teaching the circumference and area of circles.
• 🔍 The formula for the circumference of a circle is 2πr or πd, where r is the radius and d is the diameter.
• 📐 The area of a circle is calculated using the formula πr², with r being the radius.
• 📝 The value of π can be approximated as either 22/7 or 3.14 for calculations.
• 📊 The video provides examples of how to calculate the circumference when given the radius or diameter.
• 🧮 It also demonstrates how to find the radius or diameter when the circumference is known.
• 🏞️ The script includes practical examples involving the calculation of the circumference of circular areas depicted in diagrams.
• 📐 The video explains how to calculate the circumference of a circle that is part of a larger geometric shape.
• 🔢 The script uses multiplication and division to solve for the circumference and radius/diameter of circles.
• 🎓 The video concludes with a reminder to watch the next video for further learning on the area of circles.

Q & A

What is the formula to calculate the circumference of a circle?

The formula to calculate the circumference of a circle is \( C = 2\pi r \) or \( C = \pi d \) where \( r \) is the radius and \( d \) is the diameter.

What is the value of pi used in the script for calculations?

The script uses the value 22/7 for pi in some calculations, but also mentions using 3.14 when the radius or diameter is not a multiple of 7.

How do you find the circumference of a circle when the radius is given as 14 cm?

Using the formula \( C = 2\pi r \), and substituting 22/7 for pi, the calculation is \( 2 \times \frac{22}{7} \times 14 \), which simplifies to \( 2 \times 22 \times 2 \), resulting in 88 cm.

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

The formula to calculate the area of a circle is \( A = \pi r^2 \).

If the diameter of a circle is 10.5 cm, how is the circumference calculated?

The circumference is calculated using the formula \( C = \pi d \). With \( d = 10.5 \) cm and \( \pi \) approximated as 3.14, the calculation is \( 3.14 \times 10.5 \), rounded to 33 cm.

How do you determine the radius of a circle if the circumference is known?

If the circumference \( C \) is known, the radius \( r \) can be found using the rearranged formula \( r = \frac{C}{2\pi} \) or \( r = \frac{C}{2 \times \frac{22}{7}} \) if using 22/7 for pi.

What is the circumference of a circle with a circumference of 132 cm?

The script indicates that the circumference is already given as 132 cm, so no calculation is needed; the circumference is 132 cm.

How is the circumference calculated for a circle that is part of a shape in a diagram?

The script explains that if a shape in a diagram is part of a circle, such as a quarter or a half, the circumference of that part is calculated using the formula for a full circle and then adjusted according to the fraction of the circle it represents.

What is the total area of a pond shaped as a quarter circle with a radius of 1.4 m and a smaller quarter circle with a radius of 0.7 m?

The total circumference would be the sum of the circumferences of both quarter circles. For the larger, it's \( \pi \times 1.4 \), and for the smaller, it's \( \pi \times 0.7 \). The script provides the calculation as 6.6 m for the larger and 4.4 m for the smaller, totaling 11 m.

How does the script handle the calculation of the circumference of a full circle with a diameter of 22 cm?

The script uses the formula \( C = \pi d \) with \( d = 22 \) cm and \( \pi \) approximated as 3.14, resulting in \( 3.14 \times 22 \), which equals 68.68 cm when doubled for the full circle.