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555-605 (Medium)|   Geometry|      
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Bunuel
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A square is inscribed in a circle of area 18pi. Find a side of a squar 18 Mar 2018, 23:45
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B
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74% (01:19) correct 26% (01:34) wrong based on 98 sessions

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A square is inscribed in a circle of area \(18\pi\). Find a side of a square.

A. 3
B. 6
C. \(3\sqrt{2}\)
D. \(3\sqrt{2}\)
E. Cannot be determined
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B
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A square is inscribed in a circle of area 18pi. Find a side of a squar 18 Mar 2018, 23:58
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Bunuel
A square is inscribed in a circle of area \(18\pi\). Find a side of a square.

A. 3
B. 6
C. \(3\sqrt{2}\)
D. \(3\sqrt{2}\)
E. Cannot be determined
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23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



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A square is inscribed in a circle of area 18pi. Find a side of a squar 19 Mar 2018, 00:02
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Bunuel
A square is inscribed in a circle of area \(18\pi\). Find a side of a square.

A. 3
B. 6
C. \(3\sqrt{2}\)
D. \(3\sqrt{2}\)
E. Cannot be determined
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Area of circle = \(18\pi\).
so: \(\pi*R^2 = 18\pi\)
\(R^2 = 18\)
\(R = 3\sqrt{2}\)

This is the radius of the circle and also half the diagonal of the square inscribed in it.

Hence diagonal = \(6\sqrt{2}\)

Therefore - Side of square = 6

Option B.

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A square is inscribed in a circle of area 18pi. Find a side of a squar 19 Mar 2018, 14:07
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Lets first calculate the radius of the circle
Given, area of circle = 18π
so: π∗R*R=18π∗R*R=18π
R*R=18,
R=3√2

Hence the diameter= 6√2
Side of a square inscribed in a circle is Diameter/√2

=> Side of square= 6√2/√2= 6

Thus answer is B
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A square is inscribed in a circle of area 18pi. Find a side of a squar Updated on: 21 Mar 2018, 13:04
Originally posted by hawesg on 20 Mar 2018, 01:05.
Last edited by hawesg on 21 Mar 2018, 13:04, edited 2 times in total.
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I found it easiest to draw a circle with an inscribed and then create a right triangle with the two legs being equal to the radius and the hypotenuse being one of the sides of the inscribed square. Then we can solve for the hypotenuse by
a^2+b^2=c^2
c^2=36
c = 6

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A square is inscribed in a circle of area 18pi. Find a side of a squar 20 Mar 2018, 16:59
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Bunuel
A square is inscribed in a circle of area \(18\pi\). Find a side of a square.

A. 3
B. 6
C. \(3\sqrt{2}\)
D. \(3\sqrt{2}\)
E. Cannot be determined
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Since the square is inscribed in the circle, the diagonal of the square is equal to the diameter of the circle.

Let’s determine the diameter of the circle:

πr^2 = 18π

r^2 = 18

r = √9 x √2

r = 3√2, so diameter = diagonal = 6√2

Since diagonal of a square = side√2, the side of the square is 6.

Answer: B
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A square is inscribed in a circle of area 18pi. Find a side of a squar 11 Jan 2024, 09:16
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