The diameter of a circle is equal to the side of a square. The ratio of the area of the circle to the area of the square is approximately
A. pi/2
B. 2/pi
C. 2/1
D. 11/14
To find the ratio of the area of the circle to the area of the square, we need to know the formula for each of these shapes.
The formula for the area of a circle is given by:
A = πr²
where A is the area and r is the radius of the circle. Since the diameter is equal to the side of the square, the radius of the circle is half the diameter.
The formula for the area of a square is given by:
A = s²
where A is the area and s is the side length of the square.
We can now calculate the ratio of the areas:
Let's assume that the diameter of the circle is d, which is equal to the side length of the square.
Radius of the circle, r = d/2
Side length of the square, s = d
Area of the circle, A_circle = πr² = π(d/2)² = πd²/4
Area of the square, A_square = s² = d²
Ratio of the areas, A_circle/A_square = (πd²/4) / d² = π/4
Therefore, the ratio of the area of the circle to the area of the square is π/4.
Since π is approximately 3.14, π/4 is approximately 3.14/4 = 0.785.
So, the answer is not one of the given options.
circle area = π r^2
area of square = (2r)^2 = 4r^2
ratio of circle : square = πr^2 : 4r^2
= π : 4 = appr .7854
11/14 = appr .7857
evaluate the other choices.
so what do you think?