question_answer

An athletic track 14 m wide consists of two straight sections 130 m long joining semicircular ends whose inner radius in 3.5 m. The area of the shaded region is:

A)  \[4564\,{{m}^{2}}\]       

B)  \[5566.04\,{{m}^{2}}\]

C)  \[99909\,{{m}^{2}}\]                     

D) None of these

Correct Answer: A

Solution :

    Area of shaded region\[=2\times (130\times 14)+2\times \]\[\left[ \frac{1}{2}\times \frac{22}{7}\times {{(14+3.5)}^{2}}-\frac{1}{2}\times \frac{22}{7}\times {{(3.5)}^{2}} \right]\] \[=3640+\frac{22}{7}(17.5+3.5)\,(17.5-3.5)=4564\,{{m}^{2}}.\]