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प्रश्न
In the following figure, a rectangle ABCD enclosed three circles. If BC = 14 cm, find the area of the shaded portion (Take π = 22/7)
उत्तर
To calculate the area of the shaded portion, we need to subtract the total area of the three circles from the area of the rectangle.
- Length of BC (Rectangle's width): 14 cm
- The three circles are identical, and their diameters fit perfectly along the length of the rectangle (AD).
Thus: Diameter of each circle = `("Length of AD (Rectangle)")/("Number of circles")"`
`= 14/3 = 14/3 cm`
Radius of each circle = `"Diameter"/2 = 14/6 = 7/3 cm`
Step 1: Area of the rectangle
Area of Rectangle = Length × Width = AD × BC.
AD = 14 cm, BC = 14 cm.
Area of Rectangle = 14 × 14 = 96 cm2
Step 2: Total area of the three circles
Area of one circle = πr2.
`r = 7/3 cm, pi=22/7`
Area of one circle `= 22/7xx(7/3)^2=22/7xx49/9=1078/63 cm^2`
Total Area of Circles `= 3xx1078/63 = 3234/63 = 51.33 cm^2`
Step 3: Area of the shaded portion
Shaded Area = Area of Rectangle − Total Area of Circles.
Shaded Area = 196 − 51.33 = 144.67 cm2.
The area of the shaded portion is approximately: 144.67 cm2
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