Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces
Solution:
Given, four circular cardboard pieces of radii 7 cm are placed on a paper such that each piece touches the other two pieces.
We have to find the area of the portion enclosed between these pieces.
From the figure,
A, B, C and D are the four circular cardboard pieces of radii 7 cm.
On joining the centres, A, B, C and D form a square.
The side of square = 7 + 7 = 14 cm
Thus, the sides AB = AC = BD = CD = 14 cm
Area of the portion enclosed between these cardboard pieces = area of square - area of 4 sectors.
Area of square = (side)²
= (14)²
= 196 cm²
We know that the angle between the two adjacent sides of a square is 90°
So ∠A = ∠B = ∠C = ∠D = 90°
Area of sector = πr²θ/360°
Area of sector with angle A = (22/7)(7)²(90°/360°)
= (22)(7)(1/4)
= 154/4
= 38.5 cm²
Area of 4 sectors = 4(area of sector with angle A)
= 4(38.5)
= 154 cm²
Area of shaded region = 196 - 154
= 42 cm²
Therefore, the area of the shaded region is 42 cm².
✦ Try This: Four circular cardboard pieces of radii 4 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 9
Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces
Summary:
Four circular cardboard pieces of radii 7 cm are placed on a piece of paper in such a way that each piece touches the other two pieces. The area of the portion enclosed between these pieces is 42 cm²
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