Area of circle = pi * r^2
Area of circle 1 = pi * (x)^2 = pi * (x^2)
Area of circle 2 = pi * (x+1)^2 = pi * (x^2 + 2x + 1)
Area of circle 3 = pi * (x+2)^2 = pi * (x^2 + 4x + 4)
Sum of the areas = pi * (x^2) + pi * (x^2 + 2x + 1) + pi * (x^2 + 4x + 4)
= (pi)( (x^2) +(x^2 + 2x + 1) + (x^2 + 4x + 4) )
= (pi)( 3x^2 + 6x + 5)
= (3x^2)(pi) + 6x(pi) + 5(pi)
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Step-by-step explanation:
Area of circle = pi * r^2
Area of circle 1 = pi * (x)^2 = pi * (x^2)
Area of circle 2 = pi * (x+1)^2 = pi * (x^2 + 2x + 1)
Area of circle 3 = pi * (x+2)^2 = pi * (x^2 + 4x + 4)
Sum of the areas = pi * (x^2) + pi * (x^2 + 2x + 1) + pi * (x^2 + 4x + 4)
= (pi)( (x^2) +(x^2 + 2x + 1) + (x^2 + 4x + 4) )
= (pi)( 3x^2 + 6x + 5)
= (3x^2)(pi) + 6x(pi) + 5(pi)