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 π= 3.14)
![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 π= 3.14)](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/a-square-tile-of-length-20-cm-has-four-quarter-circles-1649220914.png)
Solution:
(i) Given, a square tile of length 20 cm has four quarter circles at each corner.
We have to find the area of the shaded region.
Area of shaded region = area of square tile - area of 4 quarter circles
= area of square tile - area of circle
Area of square = (side)²
Area of square tile = (20)² = 400 cm²
The length of the side of square is equal to the diameter of the circle
Diameter = 20 cm
Radius = 20/2 = 10 cm
Area of circle = πr²
= (3.14)(10)²
= 3.14(100)
= 314 cm²
Area of shaded region = 400 - 314 = 86 cm² --------------- (1)
(ii) Another square tile of length 20 cm has a circle in the centre of the tile.
We have to find the area of the shaded region.
Area of shaded region = area of square tile - area of circle
Area of square = (side)²
Area of square tile = (20)² = 400 cm²
The length of the side of the square is equal to the diameter of the circle.
Diameter = 20 cm
Radius = 20/2 = 10 cm
Area of circle = πr²
= (3.14)(10)²
= 3.14(100)
= 314 cm²
Area of shaded region = 400 - 314
= 86 cm² ------------------------- (2)
From (1) and (2),
We observe that both (i) and (ii) have the same area of the shaded region.
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☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 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 π = 3.14)
Summary:
A square tile of length 20 cm has four quarter circles at each corner as shown in Fig. 9.64(i). The area of the shaded portion is 86 cm². Another tile with the 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, the area of the shaded portion is 86 cm². The area of the shaded portion will be equal in both the cases.
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