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In the figure above, the circle is inscribed in a square tha
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18 Jul 2018, 09:38
18 Jul 2018, 09:38
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#greprepclub In the figure above, the circle is inscribed in a square.jpg [ 16.42 KiB | Viewed 10999 times ]
In the figure above, the circle is inscribed in a square that has area 16.
Quantity A |
Quantity B |
The area of the shaded region |
1 |
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.
Kudos for R.A.E
Re: In the figure above, the circle is inscribed in a square tha
[#permalink]
19 Jul 2018, 01:46
19 Jul 2018, 01:46
3
We are given that the area of the square is \(16\) hence it must be that each side of the square is \(4\)
Since the circle is inscribed in the square the diameter of the circle equals the length of a side of the square.
Therefore, the radius of the circle \(= 2\)
area of the circle is \(\pi r^2 = \pi 2^2 = 4\pi\)
subtracting area of the circle from the area of the square we get,
the combined area of the four portions outside the circle but inside the square
that area is \(16 - 4\pi\)
we are required to find the area of one of those 4 portions.
which is equal to \((16-4)\pi/4 = 4 - \pi\)
roughly \(\pi\) is \(3.14\). \(4-3.14\) = a value less than 1
Therefore option B is bigger
Since the circle is inscribed in the square the diameter of the circle equals the length of a side of the square.
Therefore, the radius of the circle \(= 2\)
area of the circle is \(\pi r^2 = \pi 2^2 = 4\pi\)
subtracting area of the circle from the area of the square we get,
the combined area of the four portions outside the circle but inside the square
that area is \(16 - 4\pi\)
we are required to find the area of one of those 4 portions.
which is equal to \((16-4)\pi/4 = 4 - \pi\)
roughly \(\pi\) is \(3.14\). \(4-3.14\) = a value less than 1
Therefore option B is bigger
Re: In the figure above, the circle is inscribed in a square tha
[#permalink]
21 Jul 2018, 03:26
21 Jul 2018, 03:26
b is greater
