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# If each shaded circular region in the figure above has radius 5, then

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Joined: 02 Sep 2009
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18 Jul 2018, 00:55
00:00

Difficulty:

5% (low)

Question Stats:

97% (00:55) correct 3% (02:00) wrong based on 31 sessions

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If each shaded circular region in the figure above has radius 5, then the total area of the shaded regions is what fraction of the area of the square region?

(A) $$\frac{\pi}{12}$$

(B) $$\frac{\pi}{36}$$

(C) $$\frac{\pi}{60}$$

(D) $$\frac{1}{6}$$

(E) $$\frac{1}{3}$$

Attachment:

Quant14.jpg [ 12.8 KiB | Viewed 474 times ]

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Updated on: 18 Jul 2018, 01:12
Bunuel wrote:

If each shaded circular region in the figure above has radius 5, then the total area of the shaded regions is what fraction of the area of the square region?

Area of each circle = π*r^2 = π*5^2 = 25π
Area of three circles = 3*25π = 75π
Area of square = S*S = 30*30 = 900

Required fraction = 75π / 900
= π/12

Hence, A.
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Originally posted by sudarshan22 on 18 Jul 2018, 01:05.
Last edited by sudarshan22 on 18 Jul 2018, 01:12, edited 1 time in total.
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18 Jul 2018, 01:11
1
sudarshan22 wrote:
Bunuel wrote:

If each shaded circular region in the figure above has radius 5, then the total area of the shaded regions is what fraction of the area of the square region?

Area of each circle = π*r^2 = π*5^2 = 25π
Area of three circles = 3*25π = 75π
Area of square = S*S = 30*30 = 900

Required fraction = 75π / 900
= π/12

Hence, E.

you mean the correct answer is A but typo
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18 Jul 2018, 01:15
Bunuel wrote:

If each shaded circular region in the figure above has radius 5, then the total area of the shaded regions is what fraction of the area of the square region?

(A) $$\frac{\pi}{12}$$

(B) $$\frac{\pi}{36}$$

(C) $$\frac{\pi}{60}$$

(D) $$\frac{1}{6}$$

(E) $$\frac{1}{3}$$

Attachment:
Quant14.jpg

Area of the square = pie $$r^2$$

But we have 3 circles having same radius .

So, 3*pie *$$(r)^2$$ = 3 *pie * $$(5)^2$$

= 75 pie

Ara of the square = 30*30 = 900

Required Fraction = pie *75 /900

= pie / 12

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18 Jul 2018, 03:44

Solution

Given:

• The radius of shaded circular region in the figure above is 5.
• Length of a side of the square= 30

To find:

• Fraction of the total area of the shaded regions to area of the square region

Approach and Working:

• Area of the square= $$30^2= 900$$
• Area of one shaded circle= $$π(5)^2= 25 π$$
o Hence, area of 3 shaded circles= $$3*25 π= 75 π$$
o Area of shaded regions to area of square region= $$\frac{75 π}{900}= \frac{25π}{300}= \frac{π}{12}$$

Hence, the correct answer is option A.

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22 Jul 2018, 18:33
Bunuel wrote:

If each shaded circular region in the figure above has radius 5, then the total area of the shaded regions is what fraction of the area of the square region?

(A) $$\frac{\pi}{12}$$

(B) $$\frac{\pi}{36}$$

(C) $$\frac{\pi}{60}$$

(D) $$\frac{1}{6}$$

(E) $$\frac{1}{3}$$

Attachment:
Quant14.jpg

The area of the shaded regions is:

3 x 5^2 x π = 75π

The area of the entire square is 30 x 30 = 900, so the shaded region as a fraction of the area of the square is:

75π/900 = 3π/36 = π/12

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Re: If each shaded circular region in the figure above has radius 5, then &nbs [#permalink] 22 Jul 2018, 18:33
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