|Class 10 Maths Areas Related to Circles||Area Related to Circle|
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.
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