question_answer

A paper is in the form of a rectangular piece ABCD in which AB = 30 cm and BC = 26 cm. A semicircular portion with BC as diameter is cut off Find the area of the remaining part.

A)  416.43 \[c{{m}^{2}}\]   

B)    620 \[c{{m}^{2}}\]      

C)    514.43 \[c{{m}^{2}}\]

D)    585.43 \[c{{m}^{2}}\]

E)                None of these

Correct Answer: C

Solution :

Area of rectangle ABCD = 30 \[\times \] 26 = 780 Diameter of the semi-circle = BC = 26 cm Area of the semi-circular portion cut off from the rectangle \[ABCD=\frac{1}{2}\times \frac{22}{7}\times 13\times 13\] \[=265.57\,c{{m}^{2}}\] \[\therefore \] Area of the remaining part = 780 - 265.57 \[=514.57\,c{{m}^{2}}\]