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For any given perimeter, the circle contains the largest area. In 3-d, a sphere will contain the largest volume. Back tro 2-d, the increase in area you get from straightening out a circle is less than the amount of are that you lose.

In terms of formulae:

circumference = 16 = 2*pi*r

so r = 8/pi

Then area = pi*r2 = pi*64/pi2 = 64/pi = 20.372 sq units

Area of a square with sides 4 = 4*4 = 16 sq units

Q: Why is the area of a circle with a circumference of 16 greater than the area of a square with sides of 4?

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The side of the square is 6. The diagonal of the square is 6 sqrt(2).The diagonal of the square is also the diameter of the circle.The circumference of the circle = pi times the diameter = 6 pi sqrt(2) = 26.657 (rounded)

Yes because the diameter of the circle is less than the sides of the square.

A circle has only one side and it is its circumference

If you know the circle's area then the radius can be found: pi*radius2 = area Divide both sides by pi: radius2 = area/pi Square root both sides: radius = the square root of (area/pi)

The sides of the Square.

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Do you mean perimeter?The sum of the lengths of the four sides of a square is the perimeterThe total length of the circumference of a circle is its perimeter

The perimeter of a circle is the circumference. If you mean the circle is drawn around (and touches the 4 corners of) a square, and you know the perimeter of the square, you divide the square's perimeter by 4, do pythagorean's theorem on the 2 sides (legs) to find the hypotenuse, and that hypotenuse will be the diameter of the circle. You then multiply that diameter you get by pi to get the circumference.

The side of the square is 6. The diagonal of the square is 6 sqrt(2).The diagonal of the square is also the diameter of the circle.The circumference of the circle = pi times the diameter = 6 pi sqrt(2) = 26.657 (rounded)

Yes because the diameter of the circle is less than the sides of the square.

Circumference refers to the distance around the outside of a circle. The distance around a square is its perimeter, which is the sum of the lengths of the four sides. Since all sides of a square are of the same length, the perimeter of a square is also four times the length of one side.

A circle has only one side and it is its circumference

If you know the circle's area then the radius can be found: pi*radius2 = area Divide both sides by pi: radius2 = area/pi Square root both sides: radius = the square root of (area/pi)

A circle has one side which is its circumference.

The sides of the Square.

NO. A square has 4 equal sides with the sides perpendicular each other. A circle has infinite sides.

If Mark makes a circle, that circle would have a circumference of 12 inches. The formula for circumference is pi times diameter, so the circumference divided by pi will give you the diameter of 3.82 inches. Divide this by 2 to get the radius of 1.91 inches. Area of a circle is pi times the radius squared. 1.91 squared is 3.6481. Multiply this by pi to get 11.46 square inches of area inside the circle. A circle is always the most efficient use of space possible given a fixed perimeter. If Mark makes a square with equal sides where all sides are 3 inches, the area would be 9 square inches. 3 X 3 = 9

One side and it is called the circumference.