Explanation:
the circumference of a circle is
C = 2×pi×r
the area is a circle is
A = pi×r²
now, we have 2 circles, A and B with radius ra and rb.
Ca = 2×pi×ra
Cb = 2×pi×rb
Cb = Ca × 0.7 (70% of circle A)
Cb / Ca = 0.7 = (2×pi×rb)/(2×pi×ra) = rb/ra
rb = 0.7 × ra
Aa = pi×ra²
Ab = pi×rb²
Aa / Ab = (pi×ra²) / (pi×rb²)
we are using the rb identity from the ra/rb ratio now in the Aa/Ab ratio :
(pi×ra²) / (pi×(0.7 × ra)²) = (pi×ra²) / (pi×0.7²×ra²) = 1/0.7² =
= 1/0.49
that means that the area of circle B is 49% of the area of circle A.