sanju09 wrote:Circle A is perfectly inscribed in a square, and the square is perfectly inscribed within circle B. The area of circle B is what percent greater than the area of circle A?
(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
Circle A:
Plug in r=1.
A = π(1^2) = π.
Square:
s = 2r = 2*1 = 2.
Diagonal = 2√2
Circle B:
R = 1/2(diagonal of square) = 1/2*(2√2) = √2.
A = π(√2)^2 = 2π.
Since Circle B is twice as big as Circle A, the area of Circle B is 100% greater.
The correct answer is
B.
To avoid making a careless error, we must understand the following distinction:
The area of Circle B is 200%
of the area of Circle A (because the area of Circle B is 2 times the area of Circle A).
The area of Circle B is 100%
greater than the area of Circle A (because we have to increase the area of Circle A by 100% to get the area of Circle B).
To be 200% greater (answer choice D), the area of Circle B would need to be 3 times the area of Circle A.
For example, if Circle A = π and Circle B = 3π, the percent increase would be:
Difference/Circle A * 100 = (3π - π)/π * 100 = 2π/π * 100 = 200%.
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percentage of square circle B greater than that of A means that A's value increased by rate (here 2)
