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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=20 m2

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.

=2015.7=4.3 m2


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

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