The ratio of the radius of circle Q to the radius of circle R is 4:5. The area of circle R is what percent greater than the area of circle Q?

Answer 1

Radius of R = r units.
Radius of Q = (4/5)*r = 4r/5 units.

Ar/Aq = pi*r^2/pi*(4r/5)^2
Ar/Aq = r^2/(4r/5)^2 = r^2/(16r^2/25)
Ar/Aq = r^2*25/16r^2 25/16 = 25/16 =
1.5625 = 156.25%

Ar = 156.25% - 100% = 56.25% > Aq.