Is the area of a circle bigger than the area of a square?

The area of a circle is πr2 , where r is the radius of the circle. But r = P/(2π), where P is the perimeter of the circle. So the area of the circle is P2 /(4π). Since 1/(4π) > (1/16), the circle has more area than the square.

Can a circle and a square have the same area?

This question is hard to understand! A square with side length 2 and a circle share the same center. That’s fine. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square.

Is the area of a rectangle bigger than the area of a circle?

4 Answers. No. The circle will always have larger area than the rectangle.

What is the relationship between the area of a square and the area of a circle?

The area of a square is equal to the area of a circle.

Is a square and circle equal?

If the side of a square is equal to the area of the circle, how do I find the ratio between the side of the square and the radius of the circle? The side of the square is equal to the square of the radius multiplied by pi.

Why circle has the largest area?

As in Lemma 2, among all plane curves of fixed length with fixed endpoints, a circular arc encloses a maximum area between it and the line joining its endpoints. Of all polygons with n sides inscribed in a given circle, the regular one has the largest area.

Does a square or circle have more area with same perimeter?

Therefore, the area of a Circle is greater than the area of a square.

How is the area of a circle similar to the area of a rectangle?

Its side is r, and its “base” is equal to the circumference of the circle, 2πr. Since the area of that rectangle is twice the area of the circle, then the area of the circle is half the base times the height.

What does the area of a circle equal to?

The area of a circle is pi times the radius squared (A = π r²).

What is the ratio of area of a circle to the area of a square whose side equals radius of circle?

Given, side of a square equals radius of a circle. where r is a radius of the circle. Now, the ratio of area of the circle to area of the square = πr2: r2 = π : 1.

What size circle will fit in a square?

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A=πr2 . Substitute r=4 in the formula.

Is the radius of a circle smaller than a square?

As others have already told you, the radius of the circle will be clearly smaller than the side of a square of equal area. What is perhaps more interesting is that the diameter of the circle will be slightly bigger (by about 12.8\%, or about one-eighth) than the side of a square of equal area.

What is the side of a square with the same area?

So the square that is the same area as the circle has sides 0.772 LONGER than the Radius of the circle. A square with side ‘d’ has area d². A circle of radius ‘r’ has area πr². So the side of the square is larger (square root of pi, or about 1.77 times larger) than the radius of the circle. An experience in the ages of medieval empires!

How do you find the area of a circle with radius?

If the circle’s radius is r, and the side of the square is a, then for the area of the circle and the square we have, respectively: Area of square = s². (Where , s= side)

How do you make two circles have the same area?

To make then have the same area, we need to make the square bigger or the circle smaller. This will result in the side of the square being longer. Given their equality that means the circle’s area will ALWAYS be larger when r = S so it follows that to have equal areas, the radius must be smaller than the side.