eyunni wrote:
Into a square with side K is inscribed a circle with radius r. If the ratio of area of square to the area of circle is P and the ratio of perimeter of the square to that of the circle is Q. Which of the following must be true?
(A) P/Q > 1
(B) P/Q = 1
(C) 1 > P/Q > 1/2
(D) P/Q = 1/2
(E) P/Q < 1/2
Area of the square = \(k^2\)
Area of the circle = \(Pi * r^2\); Diameter of the circle is k ; so the radius \(r=\frac{k}{2}\)
Area of the circle = \(pi * \frac{k^2}{4}\)
Ratio \(P = \frac{K^2}{Pi * k^2/4} = \frac{4}{Pi}\)
Perimeter of square = \(4k\)
Perimeter of circle = \(2pi*r; 2pi\) is diameter \(= k\)
Perimeter of the circle = \(pi* k\)
Ratio \(Q= \frac{4k}{pi*k} = \frac{4}{Pi}\)
Now P/Q become \(\frac{4}{pi}\) divided by \(\frac{4}{pi}\) = 1
Answer is 1
B
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