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The circumference of circle B is 70% of the circumference of circle A

Work out the ratio of the are of circle A to the area of circle B

User Anemes
by
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1 Answer

25 votes
25 votes

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.

User Aleksandr Borisov
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3.6k points