Area of Circle Examples

Let’s solve some example questions on the area of circle concepts and formulas you learnt so far :

Example 1: A large rope is in a circular shape. Its radius is 5 units. What is its area?

Solution:

A large rope is in circular shape means it is similar to circle, so we can use circle formulae to calculate the area of the large rope.

given, r = 5 units, π = 3.14

Area = 3.14 × 5 × 5
= 78.50 unit²

Thus, the area of the circle is 78.50 units²

Example 2: If the rope is in a circular shape and its diameter is 4 units. Calculate its area.

Solution:

We know that rope is in circular shape, and its diameter = 4 units
π = 3.14

Area = (3.14 /4) × 4 × 4
= 12.56 units²

Therefore, the area of the rope is 12.56 units²

Example 3: If the circumference of the circle is 8 units. Calculate its area.

Solution:

Circumference of the circle = 8 units (given)

π = 3.14

Area = 8 × 8 / (4 × 3.14)
= 5.09 units²

Therefore, the area of the circle is 5.09 units²

Example 4: Find the circumference and the area of the circle if the radius is 21 cm.

Solution:

Radius, r = 21 cm

Circumferencer of the circle = 2πr cm.

Now, substituting the value, we get

C = 2 × (22/7)× 21
C = 2×22×3
C = 132 cm

Thus, circumference of the circle is 132 cm.

Now, area of the circle = πr² cm²

A = (22/7) × 21 × 21
A = 22 × 63
A = 1386 cm²

Thus, area of the circle is 1386 cm²

Example 5: Find the area of the quadrant of a circle if its radius is 14 cm.

Solution:

Given r = 14 cm, π = 22 / 7

Area of quadrant = πr² / 4
= 22 / 7 × 14²× 1/4
= 154 cm²

Thus, the required area of quadrant = 154 cm²

Example 6: Find the area of the sector of a circle that subtends 60° angle at the center, and its radius is 14 cm.

Solution:

Given r = 14 cm, π = 22 / 7

Area of sector = (θ/360°) × πr²
= (60° / 360°) × 22 / 7 × 14²
= 102.67 cm²

Thus, the required area of quadrant = 102.67 cm²

Area of a Circle: Formula, Derivation, Examples

Area of a Circle is the measure of the two-dimensional space enclosed by a circle. It is mostly calculated by the size of the circle’s radius.

Let’s learn how to find the area of the circle using the formulas, with the help of examples.

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