Renu wants to change the design of the floor of her living room which is of dimensions 6 m 4 m and it is covered with circular tiles of diameters 50 cm each, as shown in the figure.
Number of circular tiles along length of room is
Total number of circular tiles equals
Area covered by each circular tile is
Area of rectangular floor is
Find the area of the floor that remains uncovered with tiles.
Answers
Answer:
As the diameter of circular tile is 50cm each, then radius=
2
0.5
=0.25m
Number of tiles lengthwise =
0.5m
5
=10tiles
Number of tiles widthwise =
0.5m
4
=8tiles
So, 10 tiles are length wise and 8 tiles are width wise.
So, total number of tiles =10×8=80
∴ Area of floor not covered by tiles
Area of rectangular floor - Area of 80 tiles
=5×4−80πr
2
=20−80×π×0.25×0.25
=20−
100×100×100
8×314×25×25
=20−
10
157
=20−15.7=4.3m
2
Hence,the area of floor not covered by tiles =4.3m
2
Given: The dimensions of the floor of the living room = 6 m × 4 m
The diameter of each circular tile = 50 cm
To find:
- Number of circular tiles along length of room
- Total number of circular tiles
- Area covered by each circular tile
- Area of rectangular floor
- The area of the floor that remains uncovered with tiles
Solution: The radius of each circular tile = 50/2 cm = 25 cm = 0.25 m
- Number of circular tiles along the length of room = 6/0.50 = 12
- Number of circular tiles along the width of room = 4/0.50 = 8
- Total number of circular tiles = 12 × 8 = 96
- The area covered by each circular tile =
× (0.25)² m²
= 3.14 × 0.0625 m²
= 0.19625 m²
- The area of the rectangular floor = 6 m × 4 m = 24 m².
- The area of the floor that remains uncovered with tiles
= 24 - (96 × 0.19625) m²
= 24 - 18.84 m²
= 5.16 m²