Area Related to Circle

We will study Circumference of circle, Area of Sector & Area of combined figures.

Circumference of circle = π * Diameter   = π * 2*Radius

π is an irrational number and its decimal expansion is non-terminating and non-recurring (non-repeating). We generally take the value of π as 22/7 or 3.14

Area of Circle = π * Radius  * Radius   = πr²

For Proofs, refer ExamFear video Lessons.

Numerical: Archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find area of each of five scoring regions.

Solution:

Radius of Gold Circle is 10.5 cm, thus area of gold circle = πr²

Or Area = π(10.5)² = 346.5 cm²

Area of the red Zone = Area of red circle – Area of Gold circle

Or Area of red Zone = π(21)²       - π (10.5)²

Or Area of red zone =  1039.5 cm²

Similarly you can find area of all the zones.

Numerical: The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Solution: Radius of wheel = 40 cm

Circumference of wheel = 2 πr  = 2 π * 40  = 80π  cm

In one rotation, wheel covers distance equal to its circumference.

Distance covered by wheel in 10 minutes with speed of 66km/hr, is given by

Distance = Speed * Time =  (66* 1000 * 100 cm/60 minutes ) * 10 minutes

Or Distance travelled = 1100000 cm

Number of Revolutions = Total Distance travelled by wheel / Distance travelled in one revolution

Or Number of revolutions = 1100000 cm /80 π cm   = 4375