**Finding the area and circumference of a circle :**

**Area : **

Area of a circle is defined as the space occupied by the circular object on a flat surface. The area of a shape can be measured by comparing the shape to squares of a fixed size.

**Circumference : **

The perimeter of a circle is called its circumference. In other words, the distance around the edge of a circle.

The measurements of perimeter use units such as centimeters, meters, kilometers, inches, feet, yards, and miles. The measurements of area use units such as square centimeters (cm²), square meters(m²), and so on.

**Example 1 :**

An irrigation sprinkler waters a circular region with a radius of 14 feet. Find the circumference of the region watered by the sprinkler. Use 22/7 for π.

**Solution : **

Use the formula.

C = 2πr

Plug 14 for r

C = 2π(14)

Plug 22/7 for π

C ≈ 2 x (22/7) x 14

Simplify

C ≈ 2 x (22/1) x 2

C ≈ 88

Hence, the circumference of the region watered by the sprinkler is about 88 feet.

**Example 2 :**

The diameter of a car wheel is 21 inches. Find the circumference of the wheel.

**Solution : **

Radius = Diameter / 2

Radius = 21/2 inches

Use the formula.

C = 2πr

Plug 21/2 for r

C = 2π(21/2)

Plug 22/7 for π

C ≈ 2 x (22/7) x (21/2)

Simplify

C ≈ 2 x (11/1) x (3/1)

C ≈ 66

Hence, the circumference of the wheel is 66 inches.

**Example 3 :**

Find the diameter, radius, circumference and area of the circle shown below. use 3.14 as an approximation for ∏.

**Solution :**

From the diagram shown above, we can see that the diameter of the circle is

d = 13 - 5 = 8 cm

The radius is one half the diameter. So, the radius is

r = d/2 = 8/2 = 4 cm

Using the formula for circumference, we have

C = 2∏r ≈ 2(3.14)4

C ≈ 25.1 cm

Using the formulas for area, we have

A = ∏r² ≈ (3.14)(4)²

A ≈ 50.24 square cm.

**Example 4 :**

A biscuit recipe calls for the dough to be rolled out and circles to be cut from the dough. The biscuit cutter has a radius of 4 cm. Find the area of the top of the biscuit once it is cut. Use 3.14 for π.

**Answer :**

**Since the top of the biscuit is in the shape of a circle, we can use area of circle formula to find area of the top of the biscuit. **

**Step 1 : **

Area of a circle = πr²

Radius is given in the question. That is 4 cm.

Plug r = 4 in the above formula.

Area of the circle = π(4)²

**Step 3 :**

Since radius is not a multiple of 7, we can use π ≈ 3.14.

Area of the circle ≈ (3.14) x (4)²

Area of the circle ≈ 3.14 x 16

Area of the circle ≈ 50.24 square cm.

The area of the biscuit is about 50.24 square cm.

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