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Question
Four circles are drawn side by side in a line and enclosed by a rectangle as shown below. If the radius of each of the circles is 3 cm, then calculate:
(i) The area of the rectangle.
(ii) The area of each circle.
(iii) The shaded area inside the rectangle.
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Solution
Given radius of a circle r = 3 cm
Diameter of the circle = 2r
= 2 × 3
= 6 cm
Breadth of the rectangle = Diamter of the circle
B = 6 cm
Length of the rectangle L = 4 × diameter of a circle
L = 4 × 6
L = 24 cm
(i) Area of the rectangle = L × B sq.units
= 24 × 6 cm2
Area of the rectangle = 144 cm2
(ii) Area of the circle = πr2 sq.units
= `22/7 xx 3 xx 3 "cm"^2`
= `198/7 "cm"^2`
= 28.28 cm2
(iii) Area of the shaded area = Area of the rectangle – Area of the 4 circles
= `144 - (4 xx 198/7) "cm"^2`
= `144 - 792/7 "cm"^2`
= 144 – 113.14 cm2
= 30.85 cm2
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