From a circular sheet of paper with a radius 20 cm, four circles of ra

Question

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

A. 1 : 3
B. 4 : 1
C. 3 : 1
D. 4 : 3
E. 2 :5

GMATinsight · Answer

Area of Cut portion  = 4*π*5^2 = 100π

Area of the complete big circle = π*20^2 = 400π

Area of UnCut portion  = π*20^2-100π = 400π-100π = 300π

Required Ratio  = (400π-100π)/100π = 3/1

Answer: Option C

ankban · Answer

Area of total portion = π20^2 = 400π
Area of cut portion = 4*5*5π = 100π
Area of uncut portion = 400π-100π = 300π

Answer = 300π÷100π = 3:1
C

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yashikaaggarwal · Answer

Won't uncut propotion will be 400π-100π = 300π?
Which will leave 3:1 ratio

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Archit3110 · Answer

total area of circular sheet ; 400pi
and area of 4 circles * 5 radius each ; (5)^2 *4 * pi ; 100pi 
un cut part will be 400pi-100pi ; 300 pi
so ratio of uncut to cut portion ; 300pi/100 pi ; 3:1
OPTION C

sujoykrdatta · Answer

Radius of the main circle = 20 => Area = pi * 400 Radii of the small circles = 5 => Area of the 4 small circles = 4 * pi * 25 = pi * 100 => Remaining area = 300 * pi => Required ratio = 3 : 1 But, let us pause for a moment to think - can we cut out 4 such circles of radius 5 units? (Note: The part below is NOT related to the question) Referring to the diagram below: The maximum radius of the small circles: 1.JPG From the blue triangle: AB = 2r * \sqrt{2} ; where r is the radius of the small circles and R is the radius of the big circle PQ = 2r * \sqrt{2} + 2r = 2R => r = \frac{R}{(1+\sqrt{2})} = \frac{20}{(1+\sqrt{2})} = 20* (\sqrt{2} - 1) = 20 * 0.4 = 8 Thus, we can always cut out 4 circles of radius 5

CAMANISHPARMAR · Answer

Won't uncut propotion will be 400π-100π = 300π? --->  You are right!

GMATinsight · Answer

yashikaaggarwal Yes you point it out right. Made the correction.

ScottTargetTestPrep · Answer

The area of the entire paper is 400π cm^2. The area of the 4 circles is 4 x 25π = 100π cm^2. Thus, the ratio of the uncut to cut portion is:

300π : 100π = 3 : 1

Answer: C

Abhishek009 · Answer

\frac{π20^2 - 4π5^2}{4π5^2}

= \frac{400π - 100π}{100π}

= \frac{300π}{100π}

= 3 : 1 , Answer must be (C)

From a circular sheet of paper with a radius 20 cm, four circles of ra

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From a circular sheet of paper with a radius 20 cm, four circles of ra

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