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# If the area of the square inscribed in the circle shown above is 36

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Math Expert
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If the area of the square inscribed in the circle shown above is 36  [#permalink]

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06 Sep 2018, 01:03
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Difficulty:

25% (medium)

Question Stats:

95% (00:45) correct 5% (01:25) wrong based on 20 sessions

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If the area of the square inscribed in the circle shown above is 36, what is the area of the circle?

A. $$9\pi$$

B. $$18\pi$$

C. $$\sqrt{72} \pi$$

D. $$4\sqrt{18} \pi$$

E. $$36\pi$$

Attachment:

image009.jpg [ 1.76 KiB | Viewed 301 times ]

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If the area of the square inscribed in the circle shown above is 36  [#permalink]

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06 Sep 2018, 01:13
Bunuel wrote:

If the area of the square inscribed in the circle shown above is 36, what is the area of the circle?

A. $$9\pi$$

B. $$18\pi$$

C. $$\sqrt{72} \pi$$

D. $$4\sqrt{18} \pi$$

E. $$36\pi$$

Attachment:
image009.jpg

side of the square = 6
diagonal of the square = diameter of the circle = a$$\sqrt{2}$$ = 6$$\sqrt{2}$$
area of the circle = $$\pi$$ 3$$\sqrt{2}$$*3$$\sqrt{2}$$ = 18$$\pi$$
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If the area of the square inscribed in the circle shown above is 36  [#permalink]

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06 Sep 2018, 03:23
+1 for B.

Area of Square = S^2 = 36 --> S = 6
Diagonal of Circle = 6√2 (Applying Pythagoras Theorem) , and Radius = 3√2 (Half a diagonal)
Therefore, Area of the circle = πr^2 = π * (3√2)^2 = π * 9 * 2 = 18π

Hence, B.
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Re: If the area of the square inscribed in the circle shown above is 36  [#permalink]

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06 Sep 2018, 07:57
Bunuel wrote:

If the area of the square inscribed in the circle shown above is 36, what is the area of the circle?

A. $$9\pi$$

B. $$18\pi$$

C. $$\sqrt{72} \pi$$

D. $$4\sqrt{18} \pi$$

E. $$36\pi$$

Attachment:
The attachment image009.jpg is no longer available

Diameter of the Circle is $$6√2$$ , Hence Raidus of the Circle is $$3√2$$

So, Area of the circle is $$π*3√2*3√2 = 18π$$, Answer must be (B)
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image001 %281%29.jpg [ 4.71 KiB | Viewed 185 times ]

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Re: If the area of the square inscribed in the circle shown above is 36 &nbs [#permalink] 06 Sep 2018, 07:57
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