Question

Question 11
Floor of a room is of dimensions $5m\times 4m$ and it is covered with circular tiles of diameters, 50 cm each as shown in figure. Find area of floor that remains uncovered with tiles (use $\pi =3.14)$)

Answer 1

[$\because diameter=2\times radius$]

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

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

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

$\therefore$ Area of floor of a room $=l\times b$

$5\times 4=20m^2$

Diameter of each circular tile = 50 cm

Number of circular tiles in each row = $\frac{500}{50}=10$

Number of circular tiles in each column = $\frac{400}{50}=8$

Total number of circular tiles inside the given rectangle = 10 $\times$ 8 = 80

$\Rightarrow$ Radius of each circular tile $=\frac{50}{2}=25cm$

$=\frac{25}{100}m=\frac{1}{4}m$

Now, area of a circular tile $=\pi (radius{)}^2$

$=314\times {\left(\frac{1}{4}\right)}^2=\frac{3.14}{16}{m}^2$

$\therefore$ Area of 80 circular tiles $=80\times \frac{3.14}{16}=5\times 3.14=15.7m^2$

[$\because$ 80 congruent circular tiles covering the floor of a room]

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

$=20-15.7=4.3m^2$

Hence, the required area of floor that remains uncovered with tiles is $4.3m^2$