Question

Question 119 (ii)

A square tile of length 20 cm has four quarter circles at each corner as shown in the figure. Another tile with same dimensions has a circle in the centre of the tile as shown in the figure.
If the circle touches all the four sides of the square tile, find the area of the shaded portion. In which tile, the area of the shaded portion will be more? $(Take,\pi =3.14)$

Answer 1

Area of shaded portion in first case = $85.71c{m}^2\approx 86c{m}^2$

Area of shaded portion in second case
= Area of square - Area of circle
$=20\times 20-\frac{22}{7}\times 10\times 10$ [$\because$ radius of circle $=\frac{1}{2}$ side of square = 10 cm]
$400-\frac{2200}{7}=\frac{600}{7}=\approx 86c{m}^2$
Hence, area in both cases is equal i.e $86c{m}^2$