A circle is inscribed in a square. Write and simplify an expression for the ratio of the area of the square to the area of the c ircle. For a circle inscribed in a square, the diameter of the circle is equal to the side length of the square.
2 answers:
Given: circle inscribed in a square. Side length of the square = diameter of the circle. Let x side length and diameter. Area of a square = x² Area of a circle = πr² r = radius ; half of the diameter. = x/2 Area of a circle = π * (x/2)² or π (x²/4) Ratio of the area of the square to the area of the circle x² : π(x²/4) or x² / πx²/4 x² * 4/πx² = 4/π
The area of a circle with a diameter <em>d</em> is
and the area of a square whose side is the diameter <em>d</em> of the circle is
.
The ratio of the area of a square to the area of a circle is
Since there is a common term on both sides, we cancel
and get the final ratio of:
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