Geometry

What is the ratio of the area of a circle to the area of a square?

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2014-08-26 21:56:47

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.

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Let's call the number 'K' ... the side of the square and the radius of the circle.-- the area of the square is [ K2 ]-- the area of the circle is [ (pi) K2 ]-- The ratio of the circle to the square is [(pi) K2 / K2 ] = pi

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.

By using the other information supplied about the circle to calculate either its radius (from which its area can be calculated) or its area (if the circle is similar to another with a given area and some ratio between the two circle is given):If the diameter is given: radius = diameter &divide; 2If the circumference is given: radius = circumference &divide; 2&pi;If the circle is similar to another circle which has a given area, and the length ratio is given; square the length ratio to get the area ratio and apply to the given area.

There is no direct ratio. The area is related to the square of the radius by the factor "pi." A = (pi) r2 (Pi is about 3.1416)

You add the area of the square with the area of the semi circle.

You find the area of the whole square first. Then you find the area of the circle inside of it And then subtract the area of the circle from the area of the square and then you get the shaded area of the square

pi is the square root of ten ---------- Incorrect. Pi is the mathematical ratio between the circumference and the diameter of a circle. Coincidentally, it is also the ratio between the area of a circle and the square of its radius. The square root to 10 is ~3.16227766, while Pi is ~3.1415926535897932

It depends on the ratio of what of the circle? Its circumference, diameter, area?

Given: a square with side = s and a circle with radius = s (radius is equal to the length of the side of the square) Areasquare = side squared = s2 Areacircle = pi times the square of the radius = pi times s2 Areasquare : areacircle = s2 : pi s2 = 1 : pi (The ratio is one to pi.)

It depends on the diameter of the circle and the width of the square, if they are the same then the answer is no. If you draw yourself a square then inscribe a circle with a radius of half the length of a side of the square, the circle will fit inside the square but the corners of the square will be outside the circle. Thus by inspection the area of the square is larger than the area of the circle.

In ratios, the ratios of areas is the square of the ratio of sides. Consider the original circle and the new larger circle formed by multiplying its radius (length) by 3: The circles have lengths in the ratio 1 : 3 &rarr; the circle have areas in the ratio 1&sup2; : 3&sup2; = 1 : 9 &rarr; The larger circle's area is 9 &times; 120 mm&sup2; = 1080 mm&sup2;

It is not. If you draw yourself a square then inscribe a circle with a radius of half the length of a side of the square, the circle will fit inside the square but the corners of the square will be outside the circle. Thus by inspection the area of the square is larger than the area of the circle.

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.

In a circle, the area of the circle is pi times the radius squared

If yo have the area of the circle, the square is irrelevant. Radius = sqrt(Area/pi)

The area of the square is 98 square cm. Assuming the shaded area is the remainder of the circle, its area is 55.9 square cm (approx).

If an equilateral triangle and a square have equal perimeters, then the ratio of the area of the triangle to the area of the square is 1:3.

There is no such thing as a "square circle". If you mean "8 square feet", that is already the area.

Area of a square = side squared Area of a circle = pi times radius squared

It means that if you take a circle and find its area, you must now find a square with the same area. We cannot square the circle.

Area of a circle = pi*radius2 The radius of the circle will be 1/2 the size of the length of a side of the square.

Beautiful problem !The circle has more area.If you have a circle and a square, with the circumference of the circle equal tothe perimeter of the square, then the area of the circle is always(4/pi) = 1.27324times as much as the area of the square.If you have some length of fence in your warehouse, the most land you canenclose with it is to set it up in a circle.

Area of circle = 78.54 sq cm =&gt; Radius of circle = 5 cm =&gt; Diameter of circle = 10 cm =&gt; Side of square = 10cm =&gt; Area of square = 100cm2

Area of a circle in square meters = pi times radius squared

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