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


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

A is the best answer.
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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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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) \(\frac{1}{3}\)


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

Answer: A
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