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

m4th-lab

17 Feb 202113:03

Summary

TLDRThis 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.

Outlines

00:00

📐 Introduction to Circle's Circumference and Area

This paragraph introduces the mathematical concepts of a circle's circumference and area. It begins with a greeting and a welcome to a math lesson, indicating that the previous video covered elements of a circle. The focus of this video is on the circumference and area of a circle. The formula for circumference is given as C = 2πR or C = πd, where R is the radius and d is the diameter. The area is calculated using the formula A = πr². The lesson then moves into solving examples, starting with finding the circumference given the radius or diameter, using the approximations π ≈ 22/7 or π ≈ 3.14. The examples include calculations for circles with specific radii and diameters, demonstrating how to apply the formulas and perform the arithmetic to find the circumference.

05:04

🏞️ Calculating the Circumference of a Circular Pond

The second paragraph delves into a practical application of the circumference formula by calculating the perimeter of a pond in a garden. The pond is depicted as a square with a circular segment, which is actually a quarter of a larger circle with a radius of 1.4 meters. The paragraph explains how to calculate the circumference of this quarter circle and another smaller quarter circle with a radius of 0.7 meters. The process involves using the full circle circumference formula C = 2πR and then adjusting for the quarter sections. The calculations are detailed, showing how to find the half circumferences of both quarter circles and then summing them up to get the total perimeter of the pond area.

10:06

🔍 Advanced Problems on Circle Circumference from Diagrams

The final paragraph presents more complex problems involving the calculation of circle circumferences based on diagrams. It includes scenarios where the diameter is given and the circumference needs to be determined, as well as situations where the circumference is known and the diameter or radius must be calculated. The paragraph also discusses how to interpret diagrams that show full and half circles, and how to calculate their circumferences accordingly. The examples involve using the full circle circumference formula and adjusting for the parts of the circle shown in the diagrams. The solutions are detailed, with a step-by-step approach to finding the circumferences and understanding how the parts of the circle relate to the whole.

Mindmap

Keywords

💡Circumference

Circumference refers to the total length of the line that forms the boundary of a circle. In the video, the concept is central as it teaches how to calculate the circumference of a circle using the formula C = 2πr, where r is the radius of the circle. The script provides examples, such as calculating the circumference of a circle with a radius of 14 cm, demonstrating the application of the formula.

💡Area

Area is the amount of space enclosed within a closed figure. The video script mentions the area of a circle, which is calculated using the formula A = πr^2, where r is the radius. The script discusses finding the area when the radius is known, which is essential for understanding the properties of circles and their applications in geometry.

💡Radius

The radius of a circle is the distance from the center of the circle to any point on the circumference. It is a fundamental concept in the video, used in the formulas for calculating both the circumference and the area of a circle. The script uses the radius in examples to compute the circle's properties, such as when determining the circumference of a circle with a given radius.

💡Diameter

The diameter of a circle is a line segment that passes through the center and whose endpoints lie on the circle, effectively spanning the widest part of the circle. The video script discusses using the diameter to find the circumference using the formula C = πd, where d is the diameter. An example from the script is calculating the circumference of a circle with a diameter of 10.5 cm.

💡Pi (π)

Pi, denoted as π, is a mathematical constant representing the ratio of a circle's circumference to its diameter. In the video, π is used in formulas to calculate the circumference and area of circles. The script mentions using the approximations 22/7 or 3.14 for π in calculations, which is essential for understanding the relationship between a circle's dimensions.

💡Formula

A formula in mathematics is a concise way of expressing information symbolically. The video script introduces formulas for calculating the circumference and area of a circle, which are fundamental in geometry. These formulas are used throughout the script to solve various problems, emphasizing the importance of formulas in mathematical calculations.

💡Approximation

An approximation is a value that is close to the exact value but is not exact. In the context of the video, approximations for π are used when the exact value is not necessary for the level of precision required. The script mentions using 22/7 or 3.14 as approximations for π, which helps in simplifying calculations without losing much accuracy.

💡Example Problems

Example problems are practical exercises used to illustrate how to apply mathematical concepts or solve real-world problems. The video script includes several example problems that demonstrate how to calculate the circumference and area of circles with given radii or diameters, helping viewers understand the application of mathematical formulas in problem-solving.

💡Multiplication

Multiplication is a mathematical operation where one number is used to count the number of times another number is added together. In the video, multiplication is used in the formulas for circumference and area, such as multiplying π by the radius or diameter. The script shows how to multiply these values to find the circle's properties, which is a basic arithmetic skill crucial for the calculations.

💡Division

Division is the mathematical operation of splitting a quantity into a number of equal parts. The video script uses division when solving problems that require finding the radius or diameter from the circumference, such as dividing the circumference by 2π to find the radius. This operation is essential for understanding how to reverse-engineer the formulas to find unknown variables.

Highlights

Introduction to the video on learning about the circumference and area of a circle.

Explanation of the formula for the circumference of a circle using radius (C = 2πr).

Clarification that π (pi) can be approximated as 22/7 or 3.14 for calculations.

Introduction to the formula for the area of a circle (A = πr²).

Example problem solving: finding the circumference of a circle with a radius of 14 cm.

Use of the approximation 22/7 for π in calculations when the radius is a multiple of 7.

Example problem solving: calculating the circumference of a circle with a diameter of 10.5 cm.

Explanation of using 3.14 for π when the diameter is not a multiple of 7.

Example problem solving: determining the radius of a circle given its circumference.

Methodology for solving problems involving the circumference when the diameter is given.

Example problem solving: finding the diameter of a circle with a known circumference of 154 cm.

Introduction to practical problem-solving involving the circumference of a pond shaped as a quarter circle.

Explanation of how to calculate the circumference of a quarter circle and combine it for total circumference.

Example problem solving: calculating the circumference of a pond with a specific radius using the quarter circle method.

Introduction to a problem involving the circumference of an area with a half-circle and a full circle combined.

Example problem solving: finding the total circumference of an area with a full circle and a half-circle.

Conclusion of the video with a summary of the learnings and预告 of the next video on circle area calculations.

Transcripts

00:00

Hai assalamualaikum warahmatullahi

00:02

wabarakatuh Selamat datang di

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pembelajaran matematika bersama delfini

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