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Geometry

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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?

  • Geometry -

    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.

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