Note: Figure not drawn to scale.
In the figure above, the circle has center O and has radius 10. If the length of arc (shown in bold) is between 5 and 6, what is one possible `ul("integer")` value of x ?

Answer

29, 30, 31, 32, 33 or 34

Explanation

Since the radius of the circle is 10, its circumference is ` 20 pi`. The full circumference of a circle is ` 360 ^@`. Thus an arc of length s on the circle corresponds to a central angle of ` x ^@ `, where ` ( x ) /(360) = ( s ) /(20 pi ) , or x ( 360)/(20 pi ) s`. Since ` 5 lt s lt 6`, it follows that ` ( 360 ) /(20 pi ) ( 5 ) lt x lt ( 360)/(20 pi ) ( 6 ) `, which becomes to the nearest tenth, 28.6 ` lt x lt 34.4` therefore, the possible integer value of ` x ` are 29, 30, 31, 32 , 33 and 34. any one of these numbers may be gridded as the correct answer.