NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.4

Question 11

Step 1: Convert all dimensions to the same unit.

The floor is given as \(5\,\text{m} \times 4\,\text{m}\). Since the tiles are in cm, convert the floor to cm:

\(5\,\text{m} = 500\,\text{cm}, \; 4\,\text{m} = 400\,\text{cm}.\)

Step 2: Find the area of the floor.

Area of rectangle \(= \text{length} \times \text{breadth}\).

\(500 \times 400 = 200000\,\text{cm}^2.\)

Step 3: Work out how many tiles fit.

Diameter of one tile = 50 cm ⇒ radius = 25 cm.

Along the length: \(500/50 = 10\) tiles fit.

Along the breadth: \(400/50 = 8\) tiles fit.

Total number of tiles = \(10 \times 8 = 80.\)

Step 4: Area of one circular tile.

Area = \(\pi r^2 = \pi (25)^2 = 625\pi\,\text{cm}^2.\)

Step 5: Total area of 80 tiles.

\(80 \times 625\pi = 50000\pi\,\text{cm}^2.\)

Step 6: Uncovered area.

Uncovered area = Floor area – Tile area

= \(200000 - 50000\pi\,\text{cm}^2\).

Step 7: Approximate value.

Take \(\pi \approx 3.1416\).

\(50000\pi \approx 157080.\)

Uncovered area \(= 200000 - 157080 = 42920\,\text{cm}^2.\)

Step 8: Convert back to m² (SI unit).

\(1\,\text{m}^2 = 10000\,\text{cm}^2.\)

So, \(42920\,\text{cm}^2 = 4.292\,\text{m}^2.\)