A circular floor of a building is to be tiled with ceramic tiles each of side 40 cm. If the perimeter of the floor is 66 m, calculate, correct to the nearest whole number, the number of tiles required to completely tile the floor.[take \(\pi\) = \(\frac{22}{7}\)]
Explanation
The perimeter of the circular floor, 2\(\pi\)r = 66metres
From here, we can find the radius of the circular floor.
2 x \(\frac{22}{7}\) x r = 66
44r = 66 x 7
r = \(\frac{66 \times 7}{44}\) = \(\frac{21}{2}\) m
The area of the circular floor, \(\pi\)r\(^2\) = \(\frac{22}{7}\) x (\(\frac{21}{2})^2\) = \(\frac{693}{2}\) m\(^2\)
Area of a tile, = 0.4 x 0.4 = 0.16 m\(^2\) ( since 100 cm = 1 m)
Number of tile required to tile the floor = \(\frac{\text{ Area of circular floor}}{\text{Area of a tile}}\) = \(\frac{693}{2} \div 0.16\)
= 2165.625 ≈ 2166 tiles.