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Inside a circle a square is inscribed what is the ratio of areas of the square to that circle?
Wiki User
∙ 10y ago
First we need to find the relationship between the length of a square side (x) and the radius of the circle (r). The radius of the circle is half of the diagonal of the square. Thus the length of the diagonal is 2r. Using the Pythagorean theorem, we can look at the square as two triangles where the diagonal of the square is the hypotenuse, and find the length x of the sides.
The Pythagorean theorem states that a2 + b2 = c2 for a right triangle, where c is the hypotenuse, and a and b are the other side. Since it is a square, we know a=b and thus a2 = b2.
Thus we get 2a2=c2. Since we know that c = the diagonal of the square = 2r and we defined the side of the square's length as x, we get:
2x2 = (2r)2 = 4r2
thus x2=2r2
We'll get back to that in a sec. We know the area of the circle is πr2, and the area of the square is x2, but we want these in terms of the same variable to compare them. From above, we saw that x2=2r2, so now we know that the area of the square = 2r2
To find the ratio of the square's area to the circle's area, we look at the area of the square over the area of the circle:
(2r2)/(πr2) = 2/π
Thus the ratio is 2/π.
Wiki User
∙ 10y ago
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How do you find the area of a circle without using pi?
You cannot get an accurate measure of the area without pi. If you are interested in an approximation, you could divide the circle up into tiny squares of some fixed area (their size would depend on how big the original circle was). Then count the number of squares where half or more is inside the circle and multiply by the area of each square. That will give you an estimate of the area of the circle. You could make an approximation with inscribed and circumscribed polygons (which are the sum of a number of isosceles triangles) and average the two areas, increasing the number of sides of the polygons to increase accuracy (that is the way the early Greek mathematicians did it). Much easier and quicker to use pi!
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What shape has the same perimeter but not the same area?
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For a circle inscribed in a square what is the ratio of their areas?
For a circle inside a square, the diameter is the same as the side length, and the area of the circle is about 78.54% of the square's area (pi/4). A(c) = 0.7854 A(s) The area of the square is L x L. (For a square, L = W). The area of the circle is PI x R^2, where R = L/2. Let's express the area of the square using A = L x L = (2R) x (2R) = 4 R^2 So, the ratio of the area of the circle to that of the square is: pi/4 or about 0.7854.
The side of a square is 20 cmfind the areas of the circumscribed and inscribed circles?
The radius length r of the inscribed circle equals to one half of the length side of the square, 10 cm. The area A of the inscribed circle: A = pir2 = 102pi ≈ 314 cm2 The radius length r of the circumscribed circle equals to one half of the length diagonal of the square. Since the diagonals of the square are congruent and perpendicular to each other, and bisect the angles of the square, we have sin 45⁰ = length of one half of the diagonal/length of the square side sin 45⁰ = r/20 cm r = (20 cm)(sin 45⁰) The area A of the circumscribed circle: A = pir2 = [(20 cm)(sin 45⁰)]2pi ≈ 628 cm2.
What is the ratio between side of a square and radius of circle whose areas are same?
Finding a circle with the same area as a square is known as squaring the circle. It has been proven to be impossible. (this was done in 1882) I have included some references as links to explain why this cannot be done. If you have a circle inscribed a square, then its radius is 1/2 of the side length of the square or its diameter is the length of a side. If this is what you mean then the ratio of the side of the square to the radius of the circle is 1 to 1/2 or 2 to 1.
Are the tundra areas inside the Arctic Circle?
Yes.
What is the ratio of the area of a circle to the area of a square?
Circle and square are two entirely different shapes. But the ratio of areas of square to circle if their perimeter is equal is pi/4.
How did Archimedes estimate pi?
The approximate area of the circle lies between the areas of the circumscribed and the inscribed hexagons.
What is the mathematical formula to Convert a circle diameter in millimeters to square millimeters?
No such formula exists. The diameter of a circle is a linear measure, square measure are for areas.
When a shaded circle is inside a square what fraction of the square is shaded?
It ultimately depends on the areas of the two shapes: Acircle = pi*r2 Asquare = l2 Fraction shaded = Acircle / Asquare = pi*r2/ l2 If the circle fills the square (e.g. l=2r) then the formula simplifies considerably: pi*r2/4r2 = pi/4
How do you find the area of a circle without using pi?
You cannot get an accurate measure of the area without pi. If you are interested in an approximation, you could divide the circle up into tiny squares of some fixed area (their size would depend on how big the original circle was). Then count the number of squares where half or more is inside the circle and multiply by the area of each square. That will give you an estimate of the area of the circle. You could make an approximation with inscribed and circumscribed polygons (which are the sum of a number of isosceles triangles) and average the two areas, increasing the number of sides of the polygons to increase accuracy (that is the way the early Greek mathematicians did it). Much easier and quicker to use pi!
Given a length of string L equals 50 inches construct a circle and a square such that the sum of the areas is a maximum?
Use as much of the string as is possible to make the circle. In the limit, the circumference of the circle is 50 inches and the perimeter of the square is 0. This gives a circle with an area of 198.94 sq inches and a square with an area of 0 sq inches. Any string moved from the circle to the square will reduce the total area.
What is the radius of a circle with an area of 100 meters?
It is not possible to have a circle with an area of 100 metres. Areas must be measured in square units, such as square metres. Assuming that the circle had an area of 100 sq metres, its radius would be 5.64 metres (to 2 dp).
