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The area of a circle is the space enclosed by its round boundary. We can find the area using a formula involving the radius, which is the distance from the circle’s centre to any point on the circle. The formula is pi (represented by the Greek letter π) multiplied by the radius squared (written as r^2). In other words, Area = πr². [π] is a mathematical constant roughly equal to 3.14.
| Definition | The area of a circle refers to the space enclosed by its circular shape, measured in square units. |
| Formula | There are two common formulas to calculate the area of a circle: –Area = πr², where ‘r’ represents the radius (distance from the centre to any point on the circle). –Area = π(d² / 4), where ‘d’ stands for the diameter (the distance across the circle through its centre). |
| Practical Applications | –Determining the area of circular fields or plots of land in agriculture. –Estimating the space covered by circular furniture items like tables or rugs. –Calculating the area occupied by circular objects in engineering or design projects. |
| Significance | Understanding the area of a circle helps in accurate measurement and planning, particularly in fields requiring geometric calculations. |
Table of Contents
What is Circle?
A circle is a perfectly round, flat shape with no corners or edges. Imagine a pizza – that’s a circle! Every point on the circle’s outline is the same distance from a central point, called the centre. This distance is called the radius. Circles are fundamental shapes in geometry and appear throughout various fields, from measuring areas (using the formula πr²) to representing objects like planets or coins.
Parts of Circle
This table provides information regarding the parts of a circle along with their definitions and relevant formulas:
| Part of Circle | Definition | Formula |
| Radius | The distance from the boundary of the circle to its centre. It’s represented by ‘r’ or ‘R’. | – Radius = ‘r’ or ‘R’ – Area and circumference are directly dependent on the radius. |
| Diameter | The longest chord of a circle that passes through its centre. It’s always twice the radius. | – Diameter = 2 × Radius,d = 2 × r or D = 2 × R – Radius can be calculated as: r = d/2 or R = D/2 |
| Circumference | The total length of the circle’s boundary, or its perimeter. It’s given by the formula C = 2πr. | – Circumference = 2πr |
Must Read:Area and Perimeter Questions with Answers
Area of Circle Formulas
The area of a circle shows how much space it takes up inside its boundary. This area depends on the size of the circle. If we know the radius (the distance from the centre to any point on the circle), we can easily find the area.Here are the formulas to find the area of a circle:
- If you know the radius, you can use this formula: Area = π × (radius)². Here, π is a special number, about 3.14.
- If you have the diameter (the distance across the circle through its centre), you can use this formula: Area = (π/4) × (diameter)².
- Or if you already have the circumference (the total length around the circle), you can use this formula: Area = (circumference)² / (4 × π).
So, to find the area, you just need to put the value you have, whether it’s the radius, diameter, or circumference, into one of these formulas, and you’ll get the area of the circle.
50+ Area of Circle Questions (MCQ Format)
What does the area of a circle represent?
a) The length around the circle
b) The total space enclosed by the circle’s edge
c) The distance from the centre to any point on the circle
d) The ratio of the circumference to the radius
Answer: b) The total space enclosed by the circle’s edge
What is the formula to calculate the area of a circle?
a) Area = πr²
b) Area = 2πr
c) Area = πd
d) Area = 2πd
Answer: a) Area = πr²
If the radius of a circle is 5 units, what is its area?
a) 10π square units
b) 25π square units
c) 50 square units
d) 100 square units
Answer: b) 25π square units
The area of a circle is directly proportional to:
a) The radius of the circle
b) The diameter of the circle
c) The circumference of the circle
d) The diameter squared
Answer: d) The diameter squared
What is the unit for measuring the area of a circle?
a) meters (m)
b) centimeters (cm)
c) square meters (m²)
d) Both a) and b)
Answer: c) square meters (m²)
If the diameter of a circle is 10 units, what is its area?
a) 25π square units
b) 50π square units
c) 100 square units
d) 250 square units
Answer: a) 25π square units
Which of the following is the correct formula for the circumference of a circle?
a) C = πr²
b) C = 2πr
c) C = πd
d) C = 2πd
Answer: b) C = 2πr
If the area of a circle is 36π square units, what is its radius?
a) 6 units
b) 12 units
c) 18 units
d) 24 units
Answer: a) 6 units
What happens to the area of a circle if the radius is doubled?
a) It doubles
b) It becomes four times
c) It remains the same
d) It becomes half
Answer: b) It becomes four times
If the area of a circle is 100 square units, what is its radius?
a) 5 units
b) 10 units
c) 25 units
d) 50 units
Answer: b) 10 units
Which of the following is NOT true about the area of a circle?
a) It is proportional to the square of the radius
b) It is measured in square units
c) It is half the circumference of the circle
d) It can be calculated using the formula πr²
Answer: c) It is half the circumference of the circle
What is the area of a circle if its circumference is 20π units?
a) 100 square units
b) 200 square units
c) 400 square units
d) 800 square units
Answer: a) 100 square units
Which of the following is the correct formula for the area of a circle in terms of diameter?
a) A = πr²
b) A = (π/4) × d²
c) A = C² / (4π)
d) A = 2πr
Answer: b) A = (π/4) × d²
If the area of a circle is 144 square units, what is its diameter?
a) 6 units
b) 8 units
c) 12 units
d) 16 units
Answer: c) 12 units
What happens to the area of a circle if the radius is halved?
a) It halves
b) It becomes one-fourth
c) It doubles
d) It remains the same
Answer: b) It becomes one-fourth
If the circumference of a circle is 24π units, what is its radius?
a) 6 units
b) 8 units
c) 12 units
d) 24 units
Answer: a) 6 units
What is the area of a circle if its diameter is 14 units?
a) 49π square units
b) 98π square units
c) 196 square units
d) 392 square units
Answer: c) 196 square units
Which of the following is the correct formula for the area of a circle in terms of circumference?
a) A = πr²
b) A = (π/4) × d²
c) A = C² / (4π)
d) A = 2πr
Answer: c) A = C² / (4π)
If the area of a circle is 36 square units, what is its circumference?
a) 6π units
b) 12π units
c) 18π units
d) 24π units
Answer: b) 12π units
What is the area of a circle if its circumference is 30 units?
a) 45π square units
b) 225π square units
c) 450 square units
d) 900 square units
Answer: a) 45π square units
If the radius of a circle is 7 units, what is its circumference? a) 14π units b) 21π units c) 28π units d) 49π units
Answer: c) 28π units
What is the area of a circle if its radius is 10 units?
a) 50 square units
b) 100 square units
c) 200 square units
d) 300 square units
Answer: b) 100 square units
Which of the following is the correct formula for the circumference of a circle in terms of diameter?
a) C = πr²
b) C = 2πr
c) C = πd
d) C = 2d
Answer: c) C = πd
If the area of a circle is 144π square units, what is its radius?
a) 6 units
b) 12 units
c) 18 units
d) 24 units
Answer: b) 12 units
What is the area of a circle if its diameter is 16 units?
a) 64π square units
b) 128π square units
c) 256 square units
d) 512 square units
Answer: a) 64π square units
If the circumference of a circle is 36 units, what is its diameter?
a) 6 units
b) 9 units
c) 12 units
d) 18 units
Answer: c) 12 units
What is the circumference of a circle if its area is 25π square units?
a) 5 units
b) 10 units
c) 15 units
d) 20 units
Answer: b) 10 units
If the radius of a circle is halved, what happens to its area?
a) It doubles
b) It halves
c) It becomes one-fourth
d) It remains the same
Answer: c) It becomes one-fourth
Which of the following is the correct formula for the circumference of a circle in terms of area?
a) C = πr²
b) C = 2πr
c) C = πd
d) C = 2d
Answer: d) C = 2d
If the circumference of a circle is 48π units, what is its radius?
a) 8 units
b) 12 units
c) 16 units
d) 24 units
Answer: b
What is the circumference of a circle if its area is 36 square units?
a) 6π units
b) 12π units
c) 18π units
d) 24π units
Answer: b) 12π units
If the diameter of a circle is 20 units, what is its area?
a) 100π square units
b) 200π square units
c) 400 square units
d) 800 square units
Answer: c) 400 square units
What is the radius of a circle if its area is 36π square units?
a) 6 units
b) 12 units
c) 18 units
d) 24 units
Answer: a) 6 units
If the circumference of a circle is 60 units, what is its area?
a) 900π square units
b) 1800π square units
c) 3600 square units
d) 7200 square units
Answer: a) 900π square units
Which of the following is NOT true about the area of a circle?
a) It is proportional to the square of the radius
b) It is measured in square units
c) It is half the circumference of the circle
d) It can be calculated using the formula πr²
Answer: c) It is half the circumference of the circle
What is the area of a circle if its circumference is 36π units?
a) 36 square units
b) 144 square units
c) 324 square units
d) 1296 square units
Answer: b) 144 square units
If the area of a circle is 49π square units, what is its radius?
a) 7 units
b) 14 units
c) 21 units
d) 28 units
Answer: a) 7 units
What happens to the circumference of a circle if the radius is doubled?
a) It doubles
b) It becomes four times
c) It remains the same
d) It becomes half
Answer: a) It doubles
If the radius of a circle is 9 units, what is its area?
a) 81π square units
b) 162π square units
c) 243 square units
d) 486 square units
Answer: a) 81π square units
Which of the following is the correct formula for the area of a circle in terms of circumference?
a) A = πr²
b) A = (π/4) × d²
c) A = C² / (4π)
d) A = 2πr
Answer: c) A = C² / (4π)
How to Find the Area of Circle?
In case you got above questions wrong here’s how to find the area of a circle in simple steps:
- The radius is the line segment from the centre of the circle to any point on the edge. Imagine a pizza – the distance from the centre to the crust is the radius.
- The formula for the area of a circle is A = πr², where A is the area, π (pronounced “pie”) is a constant roughly equal to 3.14, and r is the radius you measured in step 1.
- Multiply π by the radius squared (r x r). This will give you the area of the circle in square units (like square inches or square centimetres).
Difference Between Area and Circumference of Circle
In simpler terms, the circumference is like measuring the edge of the circle, while the area is like measuring the space inside the circle. The formulas and units for both are different, and they respond differently to changes in radius and diameter.
| Aspect | Circumference (C) | Area (A) |
| Definition | It’s the length around the circle, like tracing its edge. | It’s the total space enclosed by the circle’s edge. |
| Formula | Circumference (C) = 2πr | Area (A) = πr² |
| Units | It’s measured in meters, centimeters, etc. | It’s measured in meters, centimetres, etc. |
| Radius Dependence | As the radius increases, the circumference increases. | The area increases when the radius increases, but it’s proportional to the square of the radius. |
| Diameter Dependence | As the diameter increases, the circumference increases. | The area increases when the diameter increases, and it’s directly proportional to the square of the diameter. |
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FAQs
The area of circle is : Area = πr2.
The area of a circle is pi times the radius squared (A = π r²).
The Circumference (or) perimeter of circle = 2πR.Where, R is the radius of the circle.
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