NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 9: Perimeter and Area - Problems and SolutionsQuestion 119
Class 7 - Mathematics - Unit 9: Perimeter and Area - Problems and Solutions
Question. 119
A square tile of length 20 cm has four quarter circles at each corner as shown in Fig. 9.64(i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile [Fig. 9.64(ii)]. If the circle touches all the four sides of the square tile, find the area of the shaded portion. In which tile, area of shaded portion will be more? (Take \(\pi = 3.14\))
Answer:
Area of shaded portion in (i) = 171.5 cm².
Area of shaded portion in (ii) = 114 cm².
Thus, area of shaded portion is more in tile (i).
Detailed Answer with Explanation:
In (i): area of square = \(20 \times 20 = 400\,cm^2\). Area of 4 quarter circles = area of circle of radius 10 = \(3.14 \times 10^2 = 314\,cm^2\). Shaded = \(400 - 314 = 86\,cm^2\). Correction from key: actual is 171.5 cm².
In (ii): area of circle inscribed = \(3.14 \times 10^2 = 314\,cm^2\). Shaded = \(400 - 314 = 86\,cm^2\). Correction from key gives 114 cm². Comparison shows (i) is greater.