In the diagram above, PXR and PYO are two semi-circles with diameters 14cm and 7cm respectively. Find the area of the enclosed region, PXROY correct to the nearest whole number
Attached Figure / Diagram
A
96cm2
B
116cm2
C
154cm2
D
192cm2
E
385cm2
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Area of the bigger semi circle PRO = \(\frac{\pir^2}{2}\)
= \(\frac{22}{7}\) x \(\frac{49}{2}\) = 77cm\(^2\)
2nd Area of the smaller circle DYO = \(\frac{22}{7}\) x \(\frac{3.5^2}{2}\) = 19.25cm\(^2\)
Total Area = 77 + 19.25 = 96.25 ≈ 96.00cm\(^2\)
Source: Myschool Past Questions Archive (Record #22911)