Question

Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm each as shown in figure. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)

Answer 1

Given, floor of a room is covered with circular tiles.

Length of a floor of a room (l) = 5 m

And breadth of floor of a room (b) = 4 m

∴ Area of floor of a room = l × b

= 5 × 4

= 20 m²

⇒ Radius of each circular tile (r) = ${\displaystyle \frac{50}{2}\text{cm}}$

= 25 m

= ${\displaystyle \frac{25}{100}\text{m}}$

= ${\displaystyle \frac{1}{4}\text{m}}$

Now, area of a circular tile = πr²

= ${\displaystyle 3.14\times {\left(\frac{1}{4}\right)}^2{\text{m}}^2}$

= ${\displaystyle \frac{3.14}{16}{\text{m}}^2}$

∴ Number of circular tiles = 80

∴ Area of 80 circular tiles

= ${\displaystyle 80\times \frac{3.14}{16}}$ 

= 5 × 3.14

= 15.7 m²

 So, area of floor that remains uncovered with tiles = Area of floor of a room – Area of 80 circular tiles

= 20 – 15.7

= 4.3 m²

Hence, the required area of floor that remains uncovered with tiles is 4.3 m².