Question

If the radius of the circle is diminished by 20%, the area will be reduced by -​

Answer 1

Answer:

Let the radius of the circle be r

Then area of cirlce =πr

2

Given that radius of the circle is diminished by 10%

Hence the new radius =r−(10%ofr)=90%ofr=

10

9r

Area of the new circle =π(

10

9r

)

2

=

100

81

πr

2

Change in area πr

2

−

100

81

πr

2

=

100

19

πr

2

=0.19πr

2

Percentage of area diminished is 19%

Answer 2

Answer:

If the radius of a circular region were decreased by 20 percent, the area of the circular region would decrease by what percent?

If R is the original radius then the area of the circle is pi*R^2

If we decrease the radius by 20% the new radius is .8*R so the new area is:

pi*(.8*R)^2 = pi*(.64*R^2).

Compute the percent of the new to the old:

(pi*.64R^2)/(pi*R^2) = .64

The decrease then is 100 - 64 = 36%