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  • Three semicircles each of diameter 3 cm, a circle of diameter 4·5 cm and a semicircle of radius 4·5 cm are drawn in the given figure. Find the area of the shaded region. <img alt="" src="https://cdn.entrance360.com/media/uploads

Three semicircles each of diameter 3 cm, a circle of diameter 4·5 cm and a semicircle of radius 4·5 cm are drawn in the given figure. Find the area of the shaded region.

 

 

 

 
 
 
 
 

Answers (1)

There are 3 semicircles (1), (3), (4) and (5) and 1 circle (1).

Semicircle (1), (3) and (4) have radii =\frac{3}{2}=1.5 \; cm

Semicircle (5) has radius =4.5 \; cm

Circle (2) has radius =\frac{4.5}{2}=2.25 \; cm

Area of the shaded region \Rightarrow  Area of ( semicircle (5) + semicircle (3) )- semicircle (1) - semicircle (4) - circle (2))

=\frac{\pi }{2}(4.5)^2+\frac{\pi }{2}(1.5)^2-\frac{\pi }{2}(1.5)^2-\frac{\pi }{2}(1.5)^2-\pi (2.25)^2

=\pi \left [ \frac{(4.5)^2 }{2}-\frac{(1.5)^2 }{2}-(2.25)^2 \right ]

=\pi \left [ \frac{20.25 }{2}-\frac{2.25}{2}-5.0625 \right ]

=3.14\times 3.9375

=12.37\; cm^2

Posted by

Ravindra Pindel

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