math question about area of circle?

Question

if you draw a circle inside a square, is the area of the circle two thirds the area of the square?

Answer 1

No, not quite.

Take a circle of radius 1. Its area is Pi.

The corresponding square's area is 4 (2x2).

The ratio of areas is then:

Pi/4 = .7853981634, which is more than 3/4 the area of the square.

Answer 2

Let's setup an example

Let's say the side of the square is 2,
so the area is 4

If the side of the square is 2, the radius of the inscribed circle must be 1.
Area = πr² = π

The ratio of the areas is:

ratio = π/4 = 0.785

So a little more than 2/3.
.

Answer 3

No, it would be an irrational number. If the radius of the circle is r, then its diameter is 2r. Notice though that 2r would also be the length of the square. So the area of the circle is π r^2, but the area of the square is (2r)(2r) = 4r^2. So the area of the circle is actually the area of the square times π/4, not 2/3.

Answer 4

the circle will have radius r, and area pi*r^2. The square will have sides of 2r and area 4r^2. So the ratio is 4r^2/pr^2, or a ratio of 4 to pi. More like 4/3.

Answer 5

The radius of the circle = 1/2 the side of the square.

If r is the radius, circle = pi r^2 and square = (2r)(2r) = 4r^2

Answer 6

It would probably be closer to 3/4.
Suppose sides of a square are 4 units.
4*4=16
2^2*3.14 (area of circle) = ~12.56

Answer 7

no it depends on the radius and where you draw it at. i mean theres a chance it could be but yeah usually not...

Answer 8

(2*r)*(2*r)

Check out the website below, it will explain it all....

Answer 9

no i dont think so