How to find the raius of a circle

a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter.

Question:-

A sector of a circle has an area of 90 cm²and a central angle of 0.2radians .Find it's radius.


Answer:-

Area of sector = 90 cm²

Central angle = 0.2 radians

We need to convert this central angle to degrees

degrees=radians x 180/π

degrees=0.2 x 180/3.142

=11.5 degrees

                 11.5
Area of sector= -------- x area of the circle
                 360

    
             11.5
        90= ------ x πr2 
              360
The above step is having area of a circle formula
Let's find the radius (r) from the above equation

             90 x 360
            ---------- = r2
              11.5 π

          
             90 x 360
            ---------- = r2
             11.5x3.142


              896.8= r2


               r = √896.8 = 29.9

      So radius is approximately equal to 30 is the answer
We can use this in circumference of a circle formula to get the
circumference of the circle,similar ,if know the area of sector
for earth we can even find the radius of earth


                        

speed and distance question

Topic:Speed and Distance

Speed is the rate of motion, or equivalently the rate of change of distance.

If the speed of an object is given ,We can find the Distance and similarly ,if the speed has given we can find the speed as well .

Here is an example problem ...
Question : A train travels 360km at a uniform speed. If the speed had been 5km/h more it would have taken 1 hour less for the same journey. find the speed of the train?

 
Let the speed of the train be x km/hr.
Distance travelled by the train =360 km
                Distance     360
So time taken =  --------- = ----
                 speed       x
Now the new speed =(x+5)km/hr.

                        360
So the time taken will be------ hr
                        x+5

Now the new time is 1 hour lesser.

So the equation will be

    360          360
  -------  -  ------- = 1 
     x            x+5
Making the denominator equal

  360(x+5)    360x
 --------- - ------- = 1
      x       x+5
  360x+1800-360x
  ---------------  = 1
      x(x+5)
1800 = x(x+5)

 1800 = x2+5x

Quadratic formula:
        -b+√b2-4ac
 x= ----------------------
           2a

Here a=1,b=5,c=1800

      -5+√52-4*1*1800
So x= --------------------------
               2*1
       -5+√25+7200
     = -------------
            2
        -5+√7225
     = ------------
           2
         -5+85
     =   --------
            2
So   x= 40 km/hr is the Answer

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