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Area of a circle

The area of a circle is the amount of surface covered by the circular region inside its boundary.

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Student-friendly explanation

Area tells us how much flat space is enclosed by the circle. It is always written in square units such as cm², m², or mm². The radius is the most important value for finding circle area, because the formula depends directly on r.

How to write this in exams

  1. 1

    Start with the exact idea

    The area of a circle is the amount of surface covered by the circular region inside its boundary.

  2. 2

    Then show how to use it

    1. Identify the radius. 2. Square the radius carefully. 3. Multiply by π. 4. Use the value of π given in the question or standard value. 5. Write the final answer in square units.

  3. 3

    Add one concrete example

    If a circle has radius 7 cm, its area is πr² = 49π cm², which is 154 cm² using π = 22/7.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 31.4 cm² for radius 10 cm when the student multiplies π by 10 instead of 10².

Definition

The area of a circle is the amount of surface covered by the circular region inside its boundary.

Example

If a circle has radius 7 cm, its area is πr² = 49π cm², which is 154 cm² using π = 22/7.

Rule to remember

Area of circle = πr², where r is the radius. Use square units because area measures surface.

Memory hook

Radius first, then square; circle area is inside share.

Examples and method

Worked example

For r = 10 cm, area = π × 10² = 100π cm² = 314 cm² when π = 3.14.

Method to apply

1. Identify the radius. 2. Square the radius carefully. 3. Multiply by π. 4. Use the value of π given in the question or standard value. 5. Write the final answer in square units.

Diagram support

Draw a circle and shade the interior region to show that area refers to the inside space, not the boundary.

How CBSE asks it

Find the area of a circular region, compare two circles by area, or find radius when area is given.

Avoid common mistakes

Common confusion

Students sometimes use diameter instead of radius, or forget to square the radius before multiplying by π.

Common wrong answer

A common wrong answer is 31.4 cm² for radius 10 cm when the student multiplies π by 10 instead of 10².

Exam tip

When the question asks for space covered, surface area, or carpet-like covering, use area of a circle.

Quick check

A circular pond has radius 4 m. What quantity does the area of the pond measure?

The area measures the surface inside the circular boundary of the pond. For radius 4 m, you use πr² to find how much flat space the pond covers.

Answer writing and exam use

1-mark answer

The area of a circle is the amount of surface covered by the circular region inside its boundary.

2-mark answer

The area of a circle is the amount of surface covered by the circular region inside its boundary. Area of circle = πr², where r is the radius. Use square units because area measures surface. If a circle has radius 7 cm, its area is πr² = 49π cm², which is 154 cm² using π = 22/7.

3-mark answer

Area tells us how much flat space is enclosed by the circle. It is always written in square units such as cm², m², or mm². The radius is the most important value for finding circle area, because the formula depends directly on r. Area of circle = πr², where r is the radius. Use square units because area measures surface. For r = 10 cm, area = π × 10² = 100π cm² = 314 cm² when π = 3.14. Find the area of a circular region, compare two circles by area, or find radius when area is given. A common wrong answer is 31.4 cm² for radius 10 cm when the student multiplies π by 10 instead of 10².
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