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find the area of the shaded region in the following figure where PQRS is a rectangle 30 M long and the two circles have the same radii [the figure is in the attachment]
(π = 3.14)
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explaination needed
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cutygirl47:
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hey mate
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Given that the length of the rectangle is 30 cm.
On onbserving the diagram, we get that length of the rectangle is 2 times of the diameter of a circle and diameter of the circle is the breadth of the rectangle.
Now,
= > 2 × Diameter of the circle = 30 cm
= > Diameter of the circle = 15 cm
= > Radius of the circle = 7.5 cm
As Diameter of one ( any ) is equal to the breadth of the rectangle.
Breadth of the rectangle = 15 cm.
Now,
= > Area of the shaded region = area of rectangle - area of circles ( same radius & Diameter )
= > Area of the shaded region = ( 30 × 15 ) cm² - 2 × area of one circle
= > Area of the shaded region = 450 cm² - 2 × 3.14 × ( 7.5 )² cm²
= > Area of the shaded region = 450 cm² - 353.25 cm²
= > Area of shaded region = 96.75 cm²
Therefore the area of shaded region is 96.75 cm².
On onbserving the diagram, we get that length of the rectangle is 2 times of the diameter of a circle and diameter of the circle is the breadth of the rectangle.
Now,
= > 2 × Diameter of the circle = 30 cm
= > Diameter of the circle = 15 cm
= > Radius of the circle = 7.5 cm
As Diameter of one ( any ) is equal to the breadth of the rectangle.
Breadth of the rectangle = 15 cm.
Now,
= > Area of the shaded region = area of rectangle - area of circles ( same radius & Diameter )
= > Area of the shaded region = ( 30 × 15 ) cm² - 2 × area of one circle
= > Area of the shaded region = 450 cm² - 2 × 3.14 × ( 7.5 )² cm²
= > Area of the shaded region = 450 cm² - 353.25 cm²
= > Area of shaded region = 96.75 cm²
Therefore the area of shaded region is 96.75 cm².
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