SOLUTION: A circle is inscribed inside a square of which the square has side length 1 unit and the area outside the circle is painted black. Inside the circle, a square is inscribed and the

Question 1095315: A circle is inscribed inside a square of which the square has side length 1 unit and the area outside the circle is painted black. Inside the circle, a square is inscribed and the area outside the square is painted white. Inside the smaller square another circle is inscribed And that continues infinitely many times. What is the ratio of black to white area? Thank you in advance!
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Don't think that you need to find the infinite sum of all the black area and the infinite sum of all the white area. Since the same process is repeated infinitely, the ratio of black area to white area is just the ratio of black area to white area after the second square is inscribed in the first circle.

The black area at that time is the area of the first square, minus the area of the first circle. The first square has side length 1, so its area is 1. The first circle has radius 1/2, so its area is pi/4. So the black area at this point is

The first circle has area pi/4; the second square has area 1/2. So the white area at this point is

Then the ratio of black area to white area at this point -- and therefore the ratio of black area to white area in the "completed" infinite figure -- is

RELATED QUESTIONS
A square is inscribed in a circle, which in turn is inscribed in an equilateral triangle. (answered by greenestamps)

A square is inscribed in a circle. If the length of the diagonal of the square is 6.4 cm, (answered by ankor@dixie-net.com)

A circle is inscribed in a square that is 4 inches on each side. What is the area of the... (answered by greenestamps,ikleyn)

There is a square of side 6cm . A circle is inscribed inside the square. Find the ratio... (answered by unlockmath)

A circle is inscribed in a square of side 7root 2 cm. Find the total area of the four... (answered by josgarithmetic)

A circle is inscribed in a square. What percentage of the area of the square is inside... (answered by checkley71)

A circle of diameter 2 inches has its center at the center of a square of side 2 inches.... (answered by MathLover1)

A circle is inscribed inside a square that has an area of 256 in squared. What is the... (answered by Stitch)

A square is inscribed in a circle of area 18pie.Find the side of the... (answered by Cromlix,Alan3354)