A painter paints a circle. He inscribes a square w/ a side length of 1 foot inside the circle.What is the area

Answer 1

The diagonal of the square = sqrt(1^2 + 1^2) = sqrt(2).

The diagonal is the diameter of the circle.
The radius of the circle is then sqrt(2)/2
The area = pi * (sqrt(2)/2)^2 = pi * 2/4 = pi/2

Answer 2

If the side of the square is 6 cm, then that will be the same as the distance from the center of the square (where the diagonals intersect) to the midpoint of any side. The inscribed circle will be tangent to the square at the midpoint. The center of the circle will be at the same point as the center of the square. Therefore, the radius of the circle will be half the length of a side of the square, or 3 cm. The area of the square is the square of the length of a side, or 36 cm^2. The area of a circle is pi times the radius, or 3.14159 (3)^2 = 28.274. The ratio of the area of the circle to the area of the square is about 0.7854.

Answer 3

I don't have a calculator handy that will do square roots, but here's how you figure it out:

I assume the corners of the square are touching the circle and the question wants to know the area of the circle. You can draw a line through the middle of the square to make 2 right angle triangles. Figure out the length of this line using the pythagorean theorem. You already know the length of 2 sides of the triangle; they're one foot. So the diameter of the circle is the square root of 2.

Once you know the diameter of the circle, you can divide that number in half to get the radius. The formula for the area of the circle is pi multiplied by the radius squared. Plug in the numbers and you have your answer.

Answer 4

The area of the square is one foot. From the information given there is no way to calculate the area of the circle. The equation for determining the area of an object is length times width (l x w). Since a square has four EQUAL sides it is assumed that it's width is 1 foot , therefore 1x1=1. 1Lx1W=1square foot in area

Answer 5

Assuming that the four corners of the square touch the circle's edge, I would calculate the distance of two opposing corners of the square to get the diameter of the circle. then 1/2 of the diameter would be your radius, then use the old pi*r2 equation (pi time R squared) to get the circle's area.

Answer 6

the area of the circle is 1/2 pi, or pi/2

this is because the diagonal of the square would be sqrt of 2 (pythagoras or 45, 45, 90 triangle)

so, the radius is sqrt 2/2

area circle = pi*r^2

= pi * (sqrt2/2)^2
=pi * 2/4
= pi/2 ft.^2

yay!!!

Answer 7

area of the square is 1 sq. foot.

therefore: area of circle = (pi/2)*area of square=1.57 sq. ft.

its like this:
if a circle is circumscribed around a square, the area of the circle is (pi/2)*area of square.

Answer 8

the area of the square is 1 foot.

Answer 9

...Of the circle?

Well, the diagonal of the square will be sqrt(2), so the circle's area will be = pi x [(sqrt2)/2]^2

Answer 10

1/2 of a pi ft.