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Area of a square equals the area of a circle.
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28 Sep 2021, 00:33
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Question Stats:
78% (01:16) correct
21% (01:13) wrong based on 14 sessions
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Area of a square equals the area of a circle.
Quantity A
Quantity B
Perimeter of the square
Circumference of the circle
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Re: Area of a square equals the area of a circle.
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28 Sep 2021, 09:30
2
Carcass wrote:
Area of a square equals the area of a circle.
Quantity A
Quantity B
Perimeter of the square
Circumference of the circle
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Let x = the length of one side of the square. So, x² = the area of the square Also, 4x = the perimeter of the square.
Let r = the radius of the circle. So, (pi)r² = the area of the circle Also, 2(pi)r = the circumference of the circle.
So, at the moment we're comparing the following quantities: QUANTITY A: 4x QUANTITY B: 2(pi)r
If the circle and square have the same area, we can write: x² = (pi)r² Take the square root of both sides to get: x = (√pi)r
From here, we can take the x in Quantity A and replace it with its equivalent value of (√pi)r to get: QUANTITY A: 4(√pi)r QUANTITY B: 2(pi)r
Divide both quantities by 2 to get: QUANTITY A: 2(√pi)r QUANTITY B: (pi)r
Divide both quantities by r to get: QUANTITY A: 2(√pi) QUANTITY B: pi
At this point, it might be easiest to use the online calculator to evaluate the two quantities. When we do so we get the following approximations: QUANTITY A: 2(√pi) ≈ 2(1.77) ≈ 3.54 QUANTITY B: pi ≈ 3.14