ABC26GN4535 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
From a circular sheet of paper with 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)3 : 1
(c)4 : 1
(d)4 : 3
Answer
Explanation
Area of the cut portion $=\left(4 \times \frac{22}{7} \times 5 \times 5\right) \mathrm{cm}^{2}=\left(\frac{2200}{7}\right) \mathrm{cm}^{2}$. Area of the uncut portion $=\left[\left(\frac{22}{7} \times 20 \times 20\right)-\frac{2200}{7}\right] \mathrm{cm}^{2}$ $$\begin{aligned} & =\left(\frac{8800}{7}-\frac{2200}{7}\right) \mathrm{cm}^{2}=\left(\frac{6600}{7}\right) \mathrm{cm}^{2} . \\ & \therefore \text { Required ratio }=\frac{6600}{7}: \frac{2200}{7}=3: 1 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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