Question

a paper is in the form of a rectangle pqrs in which pq is equal to 10 centimetre and qr = 7cm Two semicircular portion with qr and ps as diameter are cut off find the area of the remaining part

Answer 1

Length of rectangle (PQ)= 10cm
Breadth of rectangle (QR) = 7cm 
Area of Rectangle PQRS = 10 cm * 7 cm
                                         = 70cm²
If two semicircle of Diameter QR and PS is cut
Area of remaining part = Area of the rectangle - Area of the two semicirle

Area of semicircle =  (pi * r²)/2
                             = (22/7 * 3.5 *3.5 )/2
                             = 38.5/2
                             = 19.25cm²

Area of two semicircle = 19.25 + 19.25
                                    = 38.50cm²
Area of remaining portion = 70cm² - 38.50cm²
                                         = 31.50cm²
 
∴ Area of remaining portion = 31.50cm² 

Answer 2

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