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.

Formulas for Circumference and Area 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

Substitute 14 for r. 

C  =  2π(14)

Substitute 22/7 for π. 

C  ≈  2 x (22/7) x 14

Simplify 

C  ≈  2 x (22/1) x 2

C  ≈  88

So, 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

Substitute 21/2 for r. 

C  =  2π(21/2)

Substitute 22/7 for π. 

C  ≈  2 x (22/7) x (21/2)

Simplify.

C  ≈  2 x (11/1) x (3/1)

C  ≈  66

So, 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 π.

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  =  2πr  ≈  2(3.14)4

C  ≈  25.1 cm

Using the formulas for area, we have

A  =  πr2  ≈  (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. 

Substitute 4 for r 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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