Let original diameter be x
area = [tex] \pi (x/2)^{2} [/tex]
After the original diameter has increased by 50%
x = 1.5x
area = [tex] \pi (3x/4)^{2} [/tex]
changes in area = [tex] \pi (3x/4)^{2} [/tex] - [tex] \pi (x/2)^{2}[/tex]
changes in area = [tex] \pi [(3x/4)^{2} -(x/2)^{2}][/tex]
changes in area = [tex] \pi [9x^2/16 - x^2/4][/tex]
changes in area = [tex] \pi [9x^2/16 - 4x^2/16][/tex]
changes in area = [tex] \pi [5x^2/16][/tex]
Change in area = [tex] \pi [5x^2/16][/tex] / [tex]\pi (x/2)^{2}[/tex] x 100
Change in area = [tex][5x^2/16][/tex] x [tex][4/x^2][/tex] x 100
Change in area = 5/4 x 100
Change in area = 125% (Answer D)
