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Area of a square equals the area of a circle.
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28 Sep 2021, 00:33
28 Sep 2021, 00:33
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Area of a square equals the area of a 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.
Source: manhattanreview
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.
Source: manhattanreview
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Re: Area of a square equals the area of a circle.
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28 Sep 2021, 09:30
28 Sep 2021, 09:30
2
Carcass wrote:
Area of a square equals the area of a 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.
Source: manhattanreview
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.
Source: manhattanreview
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
Answer: A
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Re: Area of a square equals the area of a circle.
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13 Sep 2023, 12:19
13 Sep 2023, 12:19
1
area of a circle = pi * r^2
area of a square = s^2
circumference of a circle = 2 * pi * r
perimeter of a square = 4s
pi* r^2 = s^2
s = r* root pi
4 * r * root pi
root pi = root 3.14 = ~ root 3 = ~1.7
4 * r * 1.7 = 6.8r
--> since we estimated using 3 for pi for the perimeter, do the same for the circumference of the circle.
2 * pi * r = 2 * 3 * r= 6r
6.8r > 6r
Choice A.
area of a square = s^2
circumference of a circle = 2 * pi * r
perimeter of a square = 4s
pi* r^2 = s^2
s = r* root pi
4 * r * root pi
root pi = root 3.14 = ~ root 3 = ~1.7
4 * r * 1.7 = 6.8r
--> since we estimated using 3 for pi for the perimeter, do the same for the circumference of the circle.
2 * pi * r = 2 * 3 * r= 6r
6.8r > 6r
Choice A.
