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1. Two equal circle are drawn in square in such a way that a side of the square forms diameter of each circle. If the remaining area of the square is 42 cm², how much will the diameter of the circle measure ?

A. 3.5 cm

B. 4 cm

C. 14 cm

D. 7.5 cm

Solution:

Let length of each side of square = 2π
According to the question,

\begin{aligned} \frac{π r^{2}}{2} + \frac{π r^{2}}{2} + 42 = Area of square \\ \Rightarrow π r^{2} + 42 = 4 r^{2} \\ \Rightarrow 4 r^{2} - π r^{2} = 42 \\ \Rightarrow r^{2} (4 - \frac{22}{7}) = 42 \\ \Rightarrow r^{2} (\frac{28 - 22}{7}) = 42 \\ \Rightarrow \frac{6 r^{2}}{7} = 42 \\ \Rightarrow r^{2} = \frac{42 \times 7}{6} \\ \Rightarrow r^{2} = 7 \times 7 \\ \Rightarrow r = 7 \\ ∴ 2 r = 14 c m \end{aligned}

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