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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 fig. Find the area of floor that remains uncovered with tiles, (Use $π = 3.14$ )

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1.9 m 2

4.8 m 2

5.2 m 2

17.2 m 2

answer is B.

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Detailed Solution

Given that the floor of a room is of dimensions

5 m × 4 m

and it is covered with circular tiles of diameters

50 cm

each.
We have to find the area of floor that remains uncovered with tiles.
Question Image

The expression to find the area of a circle is

A = π r 2

, where r is the radius of a circle.
The area of the rectangular floor,

A 1

A 1 = l × b ⇒ A 1 = 5 × 4 ⇒ A 1 = 20 m

The area covered by 77 circular tiles,

A 2

A 2 = 77 π r 2 ⇒ A 2 = 77 3.14 × 252 10000 ⇒ A 2 = 77 1962.5 10000 ⇒ A 2 = 77 0.19625 ⇒ A 2 = 15.11125

The required area can be calculated as

A r e a = A 1 − A 2 ⇒ A r e a = 20 − 15.11125 ⇒ A r e a = 4.88875 m 2

The area of the floor remains uncovered with tiles is

4.8 m 2

.
Therefore, the correct option is 2.

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