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

  1. $1:3$
  2. $4:1$
  3. $3:1$
  4. $4:3$
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First, we can draw the diagram.



We know that area of circle $ = \pi \times(\text{radius})^{2}$

Four circles are cut from the circular sheet, each has a radius $ = 5\;\text{cm}$

Area of cut out portion $ = 4 \times \pi \times(5)^{2} = 4 \times \pi \times25 = 100 \pi$

Area of uncut portion $ = $ Area of circular sheet $-$ Area of a cutout portion

$\qquad \qquad \qquad \qquad= \pi \times(20)^{2}-100 \pi = 400 \pi -100 \pi = 300 \pi $

$\therefore$ The ratio of the uncut to the cut portion $ = 300 \pi :100 \pi = 3:1$

Correct Answer $:\text{C}$

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