A circle is inscribed in a square. Write and simplify an expression for the ratio of the area of the square to the are of the circle. For a circle inscribed in a square, the diameter of the circle is equal to the side length of the square
Can someone explain pls
if the diameter of the circle is D
then the area is pi D^2 / 4
if the side of the square is D
then the area is D^2
so
area square / area circle = D^2/ (pi D^2/4) = 4/pi or about 1.27324
Sure! To find the ratio of the area of the square to the area of the circle, we need to express both areas in terms of a common variable.
Let's assume that the side length of the square is 's'.
The area of the square is given by the formula A_square = s^2.
Since the diameter of the circle is equal to the side length of the square, the radius of the circle is half the side length of the square. So, the radius of the circle is r = s/2.
The area of the circle is given by the formula A_circle = πr^2.
Substituting the value of r, we get A_circle = π(s/2)^2.
Simplifying this expression, we have A_circle = π(s^2/4).
Now, we can find the ratio of the area of the square to the area of the circle:
Ratio = A_square / A_circle
Substituting the values we derived earlier, we have:
Ratio = (s^2) / (π(s^2/4))
Simplifying this expression, we can cancel out the s^2 terms:
Ratio = 4 / π
Therefore, the simplified expression for the ratio of the area of the square to the area of the circle is 4/π.