isi-entrance 2013 Q21

isi-entrance · India 4 marks Circles Area and Geometric Measurement Involving Circles

Let $n$ be a positive integer. Consider a square $S$ of side $2n$ units. Divide $S$ into $4n^2$ unit squares by drawing $2n - 1$ horizontal and $2n - 1$ vertical lines one unit apart. A circle of diameter $2n - 1$ is drawn with its centre at the intersection of the two diagonals of the square $S$. How many of these unit squares contain a portion of the circumference of the circle?
(A) $4n - 2$
(B) $4n$
(C) $8n - 4$
(D) $8n - 2$

Let $n$ be a positive integer. Consider a square $S$ of side $2n$ units. Divide $S$ into $4n^2$ unit squares by drawing $2n - 1$ horizontal and $2n - 1$ vertical lines one unit apart. A circle of diameter $2n - 1$ is drawn with its centre at the intersection of the two diagonals of the square $S$. How many of these unit squares contain a portion of the circumference of the circle?\\
(A) $4n - 2$\\
(B) $4n$\\
(C) $8n - 4$\\
(D) $8n - 2$

Paper Questions

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