Question

The radii of two circles are in the ratio 3: 8. If the difference between their areas is 2695π cm², find the area of the smaller circle. 

Answer 1

Let the radius of the two circles be 3r and 8r respectively.

area of the circle having radius 3r = π(3r)²
                                                      = 9πr² 

area of the circle having radius 8r = π(8r)²
                                                      = 64πr²  

According to the question
64πr² - 9πr² = 2695π
              55r² = 2695
                  r² = 49
                  r = 7 cm

Hence the radius of the smaller circle is  3 x 7 = 21 cm
Area of the smaller circle is given by

A = πr² =`22/7 xx 21^2 = 1386 "cm"^2`