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Question

Find the area of the dotted portion if the dimensions are as specified in the figure. r = l4.



Correct Answer
A

21 cm2

Your Answer
B

24 cm2

Your Answer
C

28 cm2

Your Answer
D

18 cm2


Solution

The correct option is A

21 cm2


We are required to find the area of the shaded region. This can be found by subtracting the area of the 2 circles from the area of the outer rectangle.  

Here the diameter of the circle is equal to breadth of the rectangle and the length of the rectangle is equal to the 4 times the radius.

Therefore, the radius of the circle, r = 144 = 3.5 cm  

The breadth of the rectangle is = 2r  = 2 x 3.5 = 7 cm    

The area of the rectangle = length x breadth = 14x7  = 98 cm2   

The area of the circle = π×r2  = (227)×3.52=38.5cm2 

The total area of the circles is = 2 x 38.5 = 77 cm2  The area of the shaded region = Area of the rectangle – total area of the circles = 98 – 77 = 21 cm2 

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