С помощью нашего онлайн калькулятора можно найти площадь круга зная его радиус, диаметр, длину окружности.
3 основных формулы площади круга:

👉через радиус — S=πR².

👉через диаметр —

👉через длину окружности — .

Через радиус

S=πR²

Через диаметр

S=¼πd²

Через длину окружности

Круг – множество точек плоскости, удаленных от заданной точки этой плоскости (центр круг) на расстояние, не превышающее заданное (радиус круга).

Окружность – замкнутая плоская кривая, все точки которой одинаково удалены от данной точки (центра), лежащей в той же плоскости, что и кривая.

• r – радиус круга.
• d – диаметр круга.
• π (греческая буква пи) всегда равно 3,14 — обозначает константу, выражающую отношение длины окружности к его диаметру или площади круга к квадрату его радиуса.

Чтобы окончательно разобраться в теме «Круг и его площадь», смотрите видео урок на котором учитель математики понятно рассказывает все, что вам нужно знать.

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Площадь кольца — онлайн калькулятор

Чтобы найти площадь кольца, ограниченного двумя концентрическими окружностями, воспользуйтесь нашим очень удобным онлайн калькулятором:

Онлайн калькулятор

Площадь кольца по радиусам или диаметрам

Просто введите радиусы или диаметры окружностей, и получите ответ.

Площадь кольца по толщине и любому другому параметру

Просто введите толщину кольца и любой другой известный вам параметр, и получите ответ.

Теория

Площадь кольца через радиусы

Чему равна площадь кольца S ограниченного двумя окружностями, если известны радиус внешней окружности R и радиус внутренней окружности r ?

Формула

S = π ⋅ (R² — r²)

Пример

К примеру, определим площадь кольца, у которого внешний радиус R = 3 см, а внутренний радиус r = 2 см:

S = 3.14 ⋅ (3² — 2²) = 3.14 ⋅ (9 — 4) = 3.14 ⋅ 5 = 15.7 см²

Ответ: S = 15.7 см²

Площадь кольца через диаметры

Чему равна площадь кольца S ограниченного двумя окружностями, если известны диаметр внешней окружности D и диаметр внутренней окружности d ?

Формула

S = ^π/₄ ⋅ (D² — d²)

Пример

К примеру, определим площадь шайбы, внешний диаметр которой D = 4 см, а внутренний – d = 2 см:

S = 3.14 / 4 ⋅ (4² — 2²) = 0.785 ⋅ (16 — 4) = 9.42 см²

Ответ: S = 9.42 см²

Площадь кольца через толщину

Чтобы посчитать площадь кольца S зная его толщину t, необходимо знать ещё какой-нибудь из следующих параметров:

• внешний диаметр D
• внутренний диаметр d
• радиус внешней окружности R
• радиус внутренней окружности r

Формулы

S = ^π/₄ ⋅ (D² — (D — 2t)²)

S = ^π/₄ ⋅ ((d + 2t)² — d²)

S = π ⋅ (R² — (R — t)²)

S = π ⋅ ((r + t)² — r²)

Пример

Для примера, найдём чему равна площадь кольца толщиной t = 2 см и внешним диаметром D = 5 см:

S = 3.14/4 ⋅ (5² — (5 — 2 ⋅ 2)²) = 0.785 ⋅ (25 — 1) = 18.84 см²

См. также

Как найти площадь круга: формула по диаметру, радиусу

Круг – это геометрическая фигура; множество точек на плоскости, которые лежат внутри окружности.

Формула вычисления площади

1. По радиусу: 

Площадь круга (S) равняется произведению числа π и квадрата его радиуса:

S = π*r²

Радиус круга (r) – это отрезок, соединяющий его центр и любую точку на окружности.

Примечание: для расчетов значение числа π округляется до 3,14.

2. По диаметру

Площадь круга равняется одной четвертой произведения числа π и квадрата его диаметра:

Диаметр круга (d) равняется двум радиусам (d=2r). Это отрезок, который соединяет две противоположные точки на окружности.

Примеры задач

Задание 1
Найдите площадь круга, радиус которого равен 9 см.

Решение:
Используем формулу, в которой задействован радиус: S = 3,14 * (9 см)² = 254,34 см².

Задание 2
Найдите площадь круга, диаметр которого равняется 8 см.

Решение:
Применим формулу, в которой фигурирует диаметр: S = 1/4 * 3,14 * (8 см)² = 50,24 см².

90000 Arc Measure Formula | How to Find Angle Measure of an Arc (Video) 90001 90002 Arc Measure Definition 90003 90004 An arc is a segment of a circle around the circumference. An 90005 arc measure 90006 is an angle the arc makes at the center of a circle, whereas the arc length is the span along the arc. This angle measure can be in radians or degrees, and we can easily convert between each with the formula π radians = 180 °. 90007 90004 You can also measure the 90005 circumference 90006, or distance around, a circle.If you take less than the full length around a circle, bounded by two radii, you have an 90005 arc 90006. That curved piece of the circle and the interior space is called a 90005 sector 90006, like a slice of pizza. When you cut up a circular pizza, the crust gets divided into arcs. 90007 90016 90017 Arc Measure Definition 90018 90017 Arc of a Circle 90018 90017 Arc Measure vs. Arc Length 90018 90017 Degrees and Radians 90018 90017 Arc Measure Formula 90018 90017 How To Find The Measure of an Arc 90018 90017 How To Find Arc Length 90018 90017 Identifying Arc Angle Indicated 90018 90033 90002 Arc of a Circle 90003 90004 If we cut across a delicious, fresh pizza, we have two halves, and each half is an 90005 arc 90006 measuring 180 °.If we make three additional cuts in one side 90039 only (so 90040 we cut the half first into two quarters and then each quarter into two eighths), we have one side of the pizza with one big, 180 ° arc and the other side of the pizza with four, 45 ° arcs like this: 90007 90004 90043 90007 90004 The half of the pizza that is one giant slice is a 90005 major arc 90006 since it measures 180 ° (or more). The other side of the pizza has four 90005 minor arcs 90006 since they each measure less than 180 °.90007 90002 Arc Measure vs. Arc Length 90003 90004 The 90005 arc 90006 is the fraction of the circle’s circumference that lies between the two points on the circle. An arc has two measurements: 90007 90004 90058 90007 90016 90017 The 90005 arc’s length 90006 is a distance along the circumference, measured in the same units as the radius, diameter or entire circumference of the circle; these units will be linear measures, like inches, cm, m, yards, and so on 90064 90018 90017 The 90005 arc’s angle measurement 90006, taken at the center of the circle the arc is part of, is measured in degrees (or radians) 90064 90018 90033 90004 Do not confuse either arc measurement (length or angle) with the straight-line distance of a 90005 chord 90006 connecting the two points of the arc on the circle.The chord’s length will 90039 always 90040 be shorter than the arc’s length. 90007 90002 Degrees and Radians 90003 90004 To be able to calculate an arc measure, you need to understand angle measurements in both degrees and radians. An angle is measured in either degrees or radians. A circle measures 360 degrees, or 2π radians, whereas 90005 one radian equals 180 degrees 90006. So degrees and radians are related by the following equations: 90007 90004 360 ° = 2π radians 90007 90004 180 ° = π radians 90007 90004 The relationship between radians and degrees allows us to convert to one another with simple formulas.To convert degrees to radians, we take the degree measure multiplied by pi divided by 180. 90007 90004 90005 Let’s convert 90 degrees into radians for example: 90006 90007 90004 90 ° × π180 ° 90007 90004 90π180 90007 90004 π2 radians 90007 90004 90005 Now let’s convert π3 radians to degrees: 90006 90007 90004 π3 × 180π 90007 90004 180π3π 90007 90004 1803 = 60 ° 90007 90002 Arc Measure Formula 90003 90004 Once you got the hang of radians, we can use the arc measure formula which requires the arc length, s, and the radius of the circle, r, to calculate.90007 90004 arc measure = arc lengthradius = sr 90007 90116 How To Find The Measure of an Arc 90117 90004 Let’s try an example where our arc length is 3 cm, and our radius is 4 cm as seen in our illustration: 90007 90004 90121 90007 90004 Start with our formula, and plug in everything we know: 90007 90004 arc measure = sr 90007 90004 arc measure = 34 90007 90004 Now we can convert 34 radians into degrees by multiplying by 180 dividing by π. 90007 90004 34180π 90007 90004 42.9718 ≈ 43 ° 90007 90002 How To Find Arc Length 90003 90004 You need to know the measurement of the central angle that created the arc (the angle of the two radii) to calculate arc length. The arc length is the fractional amount of the circumference of the circle. The circumference of any circle is found with 2πr where r = radius. If you have the diameter, you can also use πd where d = diameter. 90007 90004 The formula for finding arc length is: 90007 .90000 Circle 90001 90002 90003 90004 90005 90004 90005 90004 90009 A circle is easy to make: 90010 90011 90009 90013 Draw a curve that is «radius» away 90010 from a central point. 90015 90011 90009 And so: 90011 90009 All points are the same distance from the center. 90011 90005 90022 90023 90009 90011 90026 You Can Draw It Yourself 90027 90009 Put a pin in a board, put a loop of string around it, and insert a pencil into the loop.Keep the string stretched and draw the circle! 90011 90009 90011 90026 Play With It 90027 90009 Try dragging the point to see how the radius and circumference change. 90011 90009 (See if you can keep a constant radius!) 90011 90026 Radius, Diameter and Circumference 90027 90009 90011 90009 The 90043 Radius 90044 is the distance from the center outwards. 90011 90009 The 90043 Diameter 90044 goes straight across the circle, through the center.90011 90009 The 90043 Circumference 90044 is the distance once around the circle. 90011 90009 And here is the really cool thing: 90011 90009 When we divide the circumference by the diameter we get 3.141592654 … 90010 which is the number π (Pi) 90011 90002 90003 90061 90009 So when the diameter is 1, the circumference is 3.141592654 … 90011 90005 90004 90005 90004 90005 90022 90023 90009 We can say: 90011 90009 Circumference = 90043 π 90044 × Diameter 90011 90077 Example: You walk around a circle which has a diameter of 100m, how far have you walked? 90078 90009 90011 90009 Distance walked = Circumference = π × 100m 90011 90009 = 90043 314m 90044 (to the nearest m) 90011 90009 Also note that the Diameter is twice the Radius: 90011 90009 Diameter = 2 × Radius 90011 90009 And so this is also true: 90011 90009 Circumference = 2 × 90043 π 90044 × Radius 90011 90009 In Summary: 90011 90002 90100 90004 × 90043 2 90044 90005 90004 × 90043 π 90044 90005 90022 90100 90004 90005 90004 90005 90022 90023 90117 90100 90004 Radius 90005 90004 Diameter 90005 90004 Circumference 90005 90022 90023 90026 Remembering 90027 90009 The length of the words may help you remember: 90011 90131 90132 90043 Radius 90044 is the shortest word and shortest measure 90135 90132 90043 Diameter 90044 is longer 90135 90132 90043 Circumference 90044 is the longest 90135 90144 90026 Definition 90027 90002 90003 90004 90005 90004 90005 90004 90009 The circle is a plane shape (two dimensional), so: 90011 90005 90022 90023 90026 Area 90027 90009 90011 90009 The area of ​​a circle is 90043 π 90044 times the radius squared, which is written: 90011 90009 A = 90043 π 90044 r 90170 2 90171 90011 90009 Where 90011 90131 90132 90043 A 90044 is the Area 90135 90132 90043 r 90044 is the radius 90135 90144 90009 To help you remember think «Pie Are Squared» (even though pies are usually round): 90011 90009 90010 90011 90077 Example: What is the area of ​​a circle with radius of 1.2 m? 90078 90009 Area = πr 90170 2 90171 90011 90009 = π × 1.2 90170 2 90171 90011 90009 = 3.14159 … × (1.2 × 1.2) 90011 90009 = 90043 4.52 90044 (to 2 decimals) 90011 90009 Or, using the Diameter: 90011 90009 90011 90009 A = (90043 π 90044/4) × D 90170 2 90171 90011 90009 90011 90077 Area Compared to a Square 90078 90009 90011 90009 A circle has 90043 about 80% 90044 of the area of ​​a similar-width square. 90010 The actual value is (π / 4) = 0.785398 … = 78.5398 …% 90011 90009 90011 90009 And something interesting for you: 90011 90009 See Circle Area by Lines 90011 90026 Names 90027 90009 Because people have studied circles for thousands of years special names have come about. 90011 90009 Nobody wants to say 90013 «that line that starts at one side of the circle, goes through the center and ends on the other side» 90015 when they can just say «Diameter». 90011 90009 So here are the most common special names: 90011 90026 Lines 90027 90009 90011 90009 A line that «just touches» the circle as it passes by is called a 90043 Tangent 90044.90011 90009 A line that cuts the circle at two points is called a 90043 Secant 90044. 90011 90009 A line segment that goes from one point to another on the circle’s circumference is called a 90043 Chord 90044. 90011 90009 If it passes through the center it is called a 90043 Diameter 90044. 90011 90009 And a part of the circumference is called an 90043 Arc 90044. 90011 90009 90011 90026 Slices 90027 90009 There are two main «slices» of a circle.90011 90009 The «pizza» slice is called a Sector. 90011 90009 And the slice made by a chord is called a Segment. 90011 90026 Common Sectors 90027 90009 The Quadrant and Semicircle are two special types of Sector: 90011 90009 90011 90009 Quarter of a circle is called a 90043 Quadrant 90044. 90011 90009 90011 90289 Half a circle is called a 90043 Semicircle. 90044 90011 90026 Inside and Outside 90027 90009 90011 90009 A circle has an inside and an outside (of course!).But it also has an «on», because we could be right on the circle. 90011 90009 Example: «A» is outside the circle, «B» is inside the circle and «C» is on the circle. 90011 90009 90011 90077 Ellipse 90078 90009 A circle is a «special case» of an ellipse. 90011 90009 90011 90009 90011 .2 $$ where r is the radius of a circle. 90007 90012 90002 Diagram 1 90007 90002 Area of ​​Circle Concept 90007 90002 The area of ​​a circle is all the space inside a circle’s circumference. In diagram 1, the area of ​​the circle is indicated by the blue color. 90007 90002 The area is not actually part of the circle. Remember a circle is just a locus of points. The area is enclosed inside that locus of points.90007 90002 90003 Interesting Fact about Circumference and Area 90006 90007 90025 90002 Explore and discover the relationship between the area formula, the radius of a circle and its graph with our interactive applet. 90007 90028 Problem 1 90029 90002 What is the area of ​​the circle in the picture? 90007 90002 Round your answer to the nearest tenth. 90007 Show Answer 90002 Remember the Formula: 90007 90002 $$ Area = \ pi \ cdot r ^ 2 \\ A = \ pi \ cdot (22 ‘) ^ 2 \\ A = \ pi \ cdot 484 \\ A = \ pi \ cdot 1520.2 \\ \ Sqrt {114.59155902616465} = r \\ r = 10.704744696916627 \ text {inches} \\ $$ 90007 90002 Now, that we have found the radius, how do we find the diameter? 90007 Answer 90002 $$ diameter = 2 \ cdot radius \\ = 2 \ cdot 10.704744696916627 \\ = 21.409489393833255 \\ \ Boxed {diameter = 21.41} \\ \ text {inches, rounded to nearest hundredth} $$ 90007 90028 Challenge Problems 90029 90002 A circle has a diameter of 12 inches. What is its area in terms of $$ \ pi $$.2 \\ A = 36 \ pi $$ 90007 90028 Problem 7 90029 90002 If a circle’s radius is doubled, then how much did its area increase? 90007 Show Answer 90002 Since the formula for the area of ​​a circle 90093 squares the radius 90094, the area of ​​the larger circle is always 4 (or 2 90009 2 90010) times the smaller circle. Think about it: You are doubling a number (which means × 2) and then squaring this (ie squaring 2) — which leads to a new area that is four times the smaller one. 90007 90002 You can see this relationship is true if you pick some actual values ​​for the radius of a circle.2 $$ 90134 90129 90120 90133 A = $$ 9 \ pi $$ 90134 90133 A = $$ 36 \ pi $$ 90134 90129 90150 90151 90002 $$ A_ {larger} 90007.90000 Exercise Worksheet for «Area of ​​a Circle Using the Diameter» 90001 Here are three randomly selected questions from a larger exercise, which can be 90002 edited 90003 and 90002 sent via e-mail 90003 to students or 90002 printed 90003 to create exercise worksheets. 90008 90009 90010 90008 off 90010 90008 on 90010 90015 90016 Finding the Area of ​​a Circle Using the Diameter (The Lesson) 90017 90008 The area of ​​a circle is found using the formula: 90010 90020 90008 In this formula, 90022 d 90023 is the diameter of the circle.The image below shows what we mean by diameter: 90010 90025 90016 90027 Interactive Widget 90017 90008 Use this 90002 interactive widget 90003 to draw a circle and then calculate its area from the diameter. Start by clicking in the shaded area. 90010 90008 90002 Oops, it’s broken! 90003 90010 90008 Turn your phone on its side to use this widget. 90010 90016 How to Find the Area of ​​a Circle Using the Diameter 90017 90008 Finding the area of ​​a circle using the diameter is easy.90010 90043 Question 90044 90008 What is the area of ​​a circle with a diameter of 10 cm, as shown below? 90010 90047 90043 Step-by-Step: 90044 90008 Start with the formula: 90010 90008 90022 Do not forget: 90023 π is pi (≈ 3.14) 90022 and 90023 d 90057 2 90058 = d × d (d squared) 90022 and 90023 / means ÷.90010 90008 Substitute the diameter into the formula. In our example, d = 10. 90010 90008 Area = π × 10 90057 2 90058 /4 90010 90008 Area = π × 10 × 10 ÷ 4 90010 90008 Area = π × 100 ÷ 4 90010 90008 Area = π × 25 90010 90008 Area = 3.14 × 25 90010 90008 Area = 78.5 cm 90057 2 90058 90010 90043 Answer: 90044 90008 The area of ​​the circle with a diameter of 10 cm is 78.5 cm 90057 2 90058. 90010 90016 Slider 90017 90008 The slider below shows another real example of how to find the area of ​​a circle using the diameter. 90010 Open the slider in a new tab 90016 How to Find the Area of ​​a Circle Using the Radius 90017 90008 The area of ​​a circle can be found using the radius rather than the diameter.90010 90008 The area of ​​a circle, using the radius, is found using the formula: 90010 90096 90008 In the formula, 90022 r 90023 is the radius of the circle. The image below shows what we mean by radius: 90010 90101 90008 Read more about how to find the area of ​​a circle using the radius 90010 90016 See Also 90017 What is a circle? What is pi? What is the diameter? Find the area of ​​a circle using the radius How to find the radius from the diameter The exponent where the base is a fraction What is the numerator? What is the denominator? .

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