Area of a Circle

Learn to calculate the space inside a circle

1. What is the Area of a Circle?

Definition

The area of a circle is the amount of space inside the circle. It is measured in square units (cm², m², etc.).

Visual: The Area

The shaded part shows the area of the circle.

2. The Area Formula

The Formula

Area = $\pi \times r \times r$

A = $\pi r^2$

where r is the radius of the circle.

Important: The formula uses the radius, not the diameter! If you’re given the diameter, you must first find the radius (r = d ÷ 2).

3. Finding Area (Radius Given)

Example 1: $(\text{Take } \pi = \frac{22}{7})$

A circle has a radius of 7 cm. Find its area.

Solution:

Area = $\pi \times r \times r$

$= \frac{22}{7} \times 7 \times 7$

$= 22 \times 7$

= 154 cm²

Tip: When the radius is 7 (or a multiple of 7), using $\pi = \frac{22}{7}$ makes the calculation easier because the 7s cancel out!

Example 2: $(\text{Take } \pi = 3.14)$

Find the area of a circular garden with radius 5 m.

Solution:

Area = $\pi \times r \times r$

= 3.14 × 5 × 5

= 3.14 × 25

= 78.5 m²

4. Finding Area (Diameter Given)

Remember!

When the diameter is given, you must first find the radius:

Radius = Diameter ÷ 2

Example: $(\text{Take } \pi = 3.14)$

The diameter of a circle is 20 cm. Find its area.

Solution:

Step 1: Find the radius

Radius = 20 cm ÷ 2 = 10 cm

Step 2: Calculate the area

Area = $\pi \times r \times r$

= 3.14 × 10 × 10

= 314 cm²

5. Practice Problems

Problem 1 $(\text{Take } \pi = \frac{22}{7})$

A circle has a radius of 14 cm. Find its area.

ShowHide solution

Area = $\pi \times r \times r$

$= \frac{22}{7} \times 14 \times 14$

$= 22 \times 2 \times 14$

= 616 cm²

Problem 2 $(\text{Take } \pi = 3.14)$

The diameter of a circular pond is 12 m. Find its area.

ShowHide solution

Radius = 12 m ÷ 2 = 6 m

Area = 3.14 × 6 × 6

= 113.04 m²

Problem 3 $(\text{Take } \pi = \frac{22}{7})$

A circular clock has a diameter of 42 cm. Find its area.

ShowHide solution

Radius = 42 cm ÷ 2 = 21 cm

Area = $\frac{22}{7} \times 21 \times 21$

$= 22 \times 3 \times 21$

= 1386 cm²

Problem 4 $(\text{Take } \pi = 3.14)$

A pizza has a radius of 15 cm. Find the area of the pizza.

ShowHide solution

Area = 3.14 × 15 × 15

= 3.14 × 225

= 706.5 cm²

Key Takeaways

Area of a circle = $\pi \times r \times r$ or $\pi r^2$

The formula always uses the radius. If the diameter is given, find the radius first (r = d ÷ 2).

Area is measured in square units (cm², m², etc.).

Use the value of π the question gives. Questions that give $\pi = \frac{22}{7}$ usually have a radius that is a multiple of 7, so the 7s cancel.

Area of a Circle

1. What is the Area of a Circle?

Definition

Visual: The Area

2. The Area Formula

The Formula

3. Finding Area (Radius Given)

Example 1: (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

Example 2: (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

4. Finding Area (Diameter Given)

Remember!

Example: (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

5. Practice Problems

Problem 1 (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

Problem 2 (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Problem 3 (Take π=227)(\text{Take } \pi = \frac{22}{7})(Take π=722​)

Problem 4 (Take π=3.14)(\text{Take } \pi = 3.14)(Take π=3.14)

Key Takeaways

Example 1: $(\text{Take } \pi = \frac{22}{7})$

Example 2: $(\text{Take } \pi = 3.14)$

Example: $(\text{Take } \pi = 3.14)$

Problem 1 $(\text{Take } \pi = \frac{22}{7})$

Problem 2 $(\text{Take } \pi = 3.14)$

Problem 3 $(\text{Take } \pi = \frac{22}{7})$

Problem 4 $(\text{Take } \pi = 3.14)$