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The area of a square and a circle are doubled
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23 Oct 2021, 13:36
23 Oct 2021, 13:36
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The area of a square with sides ‘s’ and that of a circle with radius ‘r’ is doubled.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Percentage change in the side of the square |
Percentage change in the radius of the circle |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: The area of a square and a circle are doubled
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25 Oct 2021, 14:13
25 Oct 2021, 14:13
1
So for the square case, let A = s*s, we want to find the new side b such that b*b = 2(A). Replace A with s*s and we get b^2 = 2s^2 and b = \sqrt{2}*s, so s is increased by \sqrt{2}.
For the circle, let A = pi*r^2. We want to find the new radius b such that pi*b^2 = 2(A). Replace A with pi*r^2 and we get pi*b^2 = 2*pi*r^2. We can cancel the pi's from both sides, and take square roots. Therefore, b = \sqrt{2}*r, so r is increased by \sqrt{2} == \sqrt{2}, therefore the answer is C.
For the circle, let A = pi*r^2. We want to find the new radius b such that pi*b^2 = 2(A). Replace A with pi*r^2 and we get pi*b^2 = 2*pi*r^2. We can cancel the pi's from both sides, and take square roots. Therefore, b = \sqrt{2}*r, so r is increased by \sqrt{2} == \sqrt{2}, therefore the answer is C.
gmatclubot
Re: The area of a square and a circle are doubled [#permalink]
25 Oct 2021, 14:13
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