Question 11 Floor of a room is of dimensions 5m×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 π=3.14))
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Solution
[∵diameter=2×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
∴ Area of floor of a room =l×b
5×4=20m2
Diameter of each circular tile = 50 cm
Number of circular tiles in each row = 50050=10
Number of circular tiles in each column = 40050=8
Total number of circular tiles inside the given rectangle = 10 × 8 = 80
⇒Radius of each circular tile =502=25cm
=25100m=14m
Now, area of a circular tile =π(radius)2
=314×(14)2=3.1416m2
∴ Area of 80 circular tiles =80×3.1416=5×3.14=15.7m2
[∵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=4.3m2
Hence, the required area of floor that remains uncovered with tiles is 4.3m2