Arc length, area of sector

Transcript

00:00this is question number two exercise 6.2 a central angle in a circle of radius

00:054cm is 75 degrees we have to find the length arc and area of a sector

00:13now mention the given information you have

00:17radius you have 4cm angle you have 75 degrees

00:21first of all you should know the formula l is equal to r theta

00:26this is the formula we are going to use radius you have 4cm and theta you have 75 degrees

00:35now never use angle degrees in your formula first we will convert it to mass radians

00:43how to convert? we all know that one degree is equal to pi over 180 radians

00:51now if I put value of pi as 3.1416 and divide it by 180

01:01then I will get value of one degree here that is 0.0175

01:09so basically one degree is equal to 0.0175 radians

01:16now simply what I will do

01:18I will keep radius as 4cm and 75 degrees

01:25but you want to change it to radius so you will multiply it by this value

01:30so when we multiply it we will get angle as 1.3125

01:40both these values will be multiplied and you will get answer as 5.25cm

01:53this is the length of the arc

01:56now we have to find area of a sector

01:59half r square theta

02:01half will be equal to 0.5

02:04radius you have 4 square

02:07and we have calculated theta

02:09this is our angle

02:13it was 75 degrees we converted it to radians

02:17one degree is equal to 0.0175 radians

02:21so this is our angle

02:23your angle will be 1.3125

02:28when you will multiply all these values by calculator

02:32so simply it is going to be 10.5cm square

02:36this will be your area