Question

If the radius of a circle is increased by 12% then it's area increases by

Answer 1

hey mate
here's the solution

Answer 2

Given:

The radius of a circle is increased by 12%

To Find:

Its area increases by what percent

Solution:

As we know that the area of a circle = π r²

where r is the radius

Now,

The radius is increased by 12%

So, the new radius =  r + r×12/100   [ old radius + increased radius]

                               =  112r/100

Now, the new area = π r²

                                = π (112r/100)²

                                = π (1.2544)r²

So, the percentage increased = ((new area - old area)/old area)×100

                                                  = (π (112r/100)² - πr²)/πr²

                                                   =((112)²π r² - 100²π r²)/ 100²πr²)×100

                                                   =112²-100²/100

                                                   = (112+100)(112-100)/100   [a²-b² = (a+b)(a-b)]

                                                    =212×12/100

                                                    =2544/100

                                                    = 25.44%    

Hence, its area increased by 2544 units which is 25.44%