Circles play an important role in many aspects of real-life. They are commonly used in stage and building designs, as most stages are circular or semi-circular in shape to evenly distribute sound and allow visibility from all angles. Circular structures like theaters in the round and thrust stages provide equal viewing experiences. Additionally, many everyday objects that we use are circular due to practical advantages over other shapes, such as coins, tires, and manholes.

1. (B) Mathematical Results of Geometry in Real-life Application

2. Properties of Circles…All Circles are symmetricalAll Circles do not have edgesAll Circles are proportionateAll line segments starting from the middle of the circle to the circumference is equal.

3. Real Life Applications…Circles play a really large role in our lifeWe just fail to realize it even though it is right in front of us.

4. Stage And Building Design…Stage Design refers to how a stage is constructed.Most stages are built in a circular/semi-circular manner.Some are shaped in a elliptical manner.

5. There are various theatres that employ the circular or semi-circular shape.Some Examples includeTheatres in the RoundThrust StagesTheatres…

6. Thrust Stages…Some thrust stages are formed in a semi circular mannerMusic is distributed equallyVision of performances are always equal.Theatres in the Round…Stage can be seen from all directions

7. Sound can be distributed equally

8. Adds a realistic impression to its viewers.The biggest arena in the worldCommonly used for Gladiator Fights, fights againsts beasts, executions.Influenced design of many venues.Allowed spectators to be close to the performance.Prevented performers from retreating in corner during fights..The Colosseum…

10. Common Life Applications…Things that we commonly use are round.Coins, earth, car tyres, man holes etc

11. Cars are used to travel conveniently. Car Tyres are round to decrease friction.Edges or rough parts increase friction, decreasing durability.Square tyres get worn out easily and decrease mobility.Car Tyres…

12. Earth…Gravity exists all round us.Gravity drags us and pulls us towards the centre of the earth.That’s why the earth is circular.Because the gravitational pull is constant throughout.

13. Erathothenes…He managed to calculate the earths circumference even without travelling out of Egypt. By using the fact that the earth is completely round due to the existence of an equal, constant gravity, he managed to calculate the Earth’s circumference.Manholes…Manholes are used for maintenance that needs performing on underground sewers, telephone connections, electricity, gas and storm drains. It is circular as it will not fall into the hole, whereas if it is square, it can fall diagonally.