please help me to solve this

Question

If the area of the shaded part of R is 14π, what is the value of x?

1. A.
2. 2
3. 
   
4. B.
5. 3
6. 
   
7. C.
8. 4
9. 
   
10. D.
11. 1

Answer 1

Circle's area = pi(r^2)

IF the shaded area = 14pi

the shaded area would then be 14pi/pi(r^2) = 14/r^2 as a fraction of the circle's area

if r=1, 2, or 3, that's more area than the circle, as 14/1, 14/4 or 14/9 are all >1

if x = r then 14/16 = 7/8 of the circle which looks roughly like it might be the Circle's area minus the area of the sector SRW

so conjecture is C 4 is the answer

Sometimes the problem is figuring out what the problem is, as no "x" or "shaded" area appears in the diagram, unless you update it.