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Sub 505 (Easy)|   Geometry|      
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Bunuel
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If each shaded circular region in the figure above has radius 5, then 18 Jul 2018, 00:55
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5% (low)

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98% (01:03) correct 3% (02:00) wrong based on 43 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) \(\frac{1}{3}\)


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A
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If each shaded circular region in the figure above has radius 5, then Updated on: 18 Jul 2018, 01:12
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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Bunuel

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?
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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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If each shaded circular region in the figure above has radius 5, then 18 Jul 2018, 01:11
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sudarshan22
Bunuel

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.
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you mean the correct answer is A but typo
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If each shaded circular region in the figure above has radius 5, then 18 Jul 2018, 01:15
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Bunuel

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


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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

A is the best answer.
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If each shaded circular region in the figure above has radius 5, then 18 Jul 2018, 03:44
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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.

Answer: A
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If each shaded circular region in the figure above has radius 5, then 22 Jul 2018, 18:33
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Bunuel

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


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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

Answer: A
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