. 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.

semicircles

 

Best Answer

Explanation

We know the formula for area of the circle isr2.

And area of semi circle is πr2/2.

Now we divide the given figure into 2 circles and 2  semi circle.

Circle 1 has radius  4.5 /2=2.25cm and 

Circle 2 has radius 3 /2=1.5 cm.

Semi circle 1 has radius 4.5 /cm

Semi circle 2  has radius 3 /2=1.5 cm 

Now area of circle 1 will be 

π(2.25)2=5.6025π

Similarly area of circle 2 will be 

(1.5)2=2.25

Area of Semi circle 1 is π(4.5)2 /2=10.125 

Area of semi circle  2 is π(1.5)2 /2=1.125

Now area of shaded region thus formed will be

Area of semi circle  1 + Area of semi circle 2- area of circle 1-area of circle 2

=π(10.125+1.125-5.6025-2.25)

=π(3.3975)

Final Answer

The area of shaded region is 3.3975π=10.66185 cm2.

 

 

Talk to Our counsellor