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. 11.18. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)
Solution:
Given, the floor of a room with dimensions 5 m × 4 m is covered with circular tiles of diameters 50 cm.
We have to find the area of the floor that remains uncovered with tiles.
Area of floor of a room = length × breadth
= 5 × 4
= 20 m²
Given, diameter of each circular tile = 50 cm
Number of tiles in each row = 5m/50cm
1 m = 100 cm
= 500/50
= 10
Number of tiles in each column = 4m/50cm
= 400/50
= 8
Total number of tiles in the floor = 10 × 8 = 80
Radius of tiles = 50/2 = 25 cm
r = 25/100
r = 0.25 m
Area of circle = πr²
Area of circular tile = (3.14)(0.25)²
= 0.19625 m²
Area of 80 tiles = 80(area of one tile)
= 80(0.196)
= 15.7 m²
Area of the floor that remains uncovered with the tiles = area of floor - area of 80 tiles
= 20 - 15.7
= 4.3 m²
Therefore, the area of the floor that remains uncovered with the tiles is 4.3 m².
✦ Try This: Floor of a room is of dimensions 6 m × 3 m and it is covered with circular tiles of diameters 20 cm each as shown in Fig. 11.18. Find the area of the floor that remains uncovered with tiles. (Use π = 3.14)
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 11
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. 11.18. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)
Summary:
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. 11.18. The area of floor that remains uncovered with tiles is 4.3 m²
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