question_answer

An athletic track 14 m wide consists of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. The area of the track is

A)  \[7056\,\,{{m}^{2}}\] 

B)  \[7016\,\,{{m}^{2}}\]

C)  \[7076\,\,{{m}^{2}}\] 

D)  \[7006\,\,{{m}^{2}}\]

Correct Answer: A

Solution :

[a]        The area of the track \[=(120\times 98-120\times 70)+2\cdot \frac{1}{2}\pi \left[ {{49}^{2}}-{{35}^{2}} \right]\] \[=3360+3696=7056\,{{m}^{2}}\]