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# A square is inscribed in a circle of area 18pi. Find a side of a squar

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
A square is inscribed in a circle of area 18pi. Find a side of a squar  [#permalink]

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18 Mar 2018, 23:45
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Difficulty:

35% (medium)

Question Stats:

69% (01:15) correct 31% (01:31) wrong based on 57 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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Joined: 02 Sep 2009
Posts: 58434
Re: A square is inscribed in a circle of area 18pi. Find a side of a squar  [#permalink]

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18 Mar 2018, 23:58
Bunuel wrote:
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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Re: A square is inscribed in a circle of area 18pi. Find a side of a squar  [#permalink]

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19 Mar 2018, 00:02
Bunuel wrote:
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

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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Re: A square is inscribed in a circle of area 18pi. Find a side of a squar  [#permalink]

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19 Mar 2018, 14:07
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

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A square is inscribed in a circle of area 18pi. Find a side of a squar  [#permalink]

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Updated on: 21 Mar 2018, 13:04
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

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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Re: A square is inscribed in a circle of area 18pi. Find a side of a squar  [#permalink]

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20 Mar 2018, 16:59
Bunuel wrote:
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

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.

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Re: A square is inscribed in a circle of area 18pi. Find a side of a squar   [#permalink] 20 Mar 2018, 16:59
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