A circular playground for a daycare center is to be covered with square tiles that are 9 inches on each side. The circle has a diameter of 12 ft. The tiles are packaged in boxes of 25 tiles. How many boxes of tiles are needed?

Answer 1

First, we need to calculate the area of the circular playground.

The radius of the circle is half of the diameter, so the radius is 12 ft / 2 = 6 ft.

The area of a circle is πr^2, so the area of the playground is π(6^2) = 36π square feet.

We now need to convert the area into square inches since each tile is measured in square inches.

1 square foot = 144 square inches, so 36π square feet = 36π * 144 square inches = 5184π square inches.

Since each tile is 9 inches on each side, the area covered by each tile is 9 * 9 = 81 square inches.

Now, we divide the total area of the playground by the area covered by each tile to find out how many tiles are needed: 5184π / 81 = 64π tiles.

Since each box contains 25 tiles, we divide the total number of tiles needed by the number of tiles in each box to find out how many boxes are needed: 64π / 25 ≈ 8.06 boxes.

Since we cannot have a fraction of a box, we need to round up to the nearest whole number. So, we will need 9 boxes of tiles to cover the circular playground.