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


                        

Evaluating Area of Triangle using Integration

Here is a Multi choice question to Evaluate Area of Triangle by Integration. You can find similar set of questions at TutorVista Blogs.

Topic : Area of Triangle by Integration

Below example will help you to identify correct choice and get reasons for, why remaining choices are incorrect.

Question : use the graph of Integrand and area to evaluate the integral ₂∫⁴ (x/2 + 3) dx

a) 21
b) 29
c) 17
d) 46

Solution :
Choice (a) is correct.
y = x/2 + 3 is a straight line above x-axis for x ≥ -6














₂∫⁴ (x/2 + 3) dx = = area of quadrilateral DBCE= area of the triangle ACE – area of the triangle ABD

= 1/2 * 5 * 10 - 1/2 * 2 * 4 = 25 - 4 = 21

choice b is incorrect because of the error in adding the areas of the triangles ACE and ABD instead of subtracting.

Choice c is incorrect because of the error in missing to divide 8 by 2 in the area of the triangle ABD.

Choice d is incorrect because of the error in missing to divide 50 by 2 in the area of the triangle ACE.

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