Question

A circular floor with a radius 28cm is tiled with 30 square tiles of side 8 cm as shown in the figure find the area of the shaded region.

Answer 1

Hint: To find the area of the shaded region we first need to calculate the portion covered by the 30 tiles.
Then we need to calculate the area of the circle.

The shaded region is the area we will get by subtracting the total area covered by the 30 square tiles from the area of the circle.

Formula used:
The area of a circle with radius r is \[\pi {r^2}\]
The area of a square with side a is \[{a^2}\]

Complete step by step solution:
It is given that the circular floor has a radius of 28cm.
That is\[r = 28cm\] .
Let us now find the value of the area of the floor,
Thus the area of the circular floor is given by\[\pi {r^2}\]
Substituting the known values we get,
Area of the circular floor \[ = \dfrac{{22}}{7} \times 28 \times 28\]
\[ = 2464c{m^2}\]
Also given that, the circular floor is tiled with 30 square tiles of side 8cm.
Here it is given that the side of the square floor is 8 cm.
That is \[a = 8cm\]
We know that the area of one tiles is \[{a^2}\]
This implies area of one tile\[ = {8^2} = 64c{m^2}\]
The total area of the tiled portion covered by 30 square tiles is \[30 \times 64 = 1920c{m^2}\]
Thus the area of the shaded region is = area of the circular floor – area of the portion covered by the 30 tiles
The area of the shaded region\[ = \left( {2464 - 1920} \right)c{m^2}\]
This implies the area of the shaded region\[ = 544c{m^2}\]

$\therefore$ Hence, the area of the shaded region is \[544c{m^2}\].

Note:
Here we will find the area of one tile initially we should be careful that there is 30 tile in the room, therefore, we should multiply the area of one tile with 30. This is more important in finding the area of the shaded region.