question_answer

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

A)  \[=\frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi \times {{\left( \frac{x}{4\pi } \right)}^{3/2}}\]               

B)  \[=\frac{4}{3}\pi \times \frac{x}{4\pi }\sqrt{\frac{x}{4\pi }}=\frac{x}{3}\sqrt{\frac{x}{4\pi }.}\]

C)  \[\frac{\frac{4}{3}\pi {{r}^{3}}}{\frac{4}{3}\pi {{(21-r)}^{3}}}=\frac{64}{27}\]               

D) None of these

Correct Answer: A

Solution :

Area of shaded region \[130\sqrt{2}m\] \[72c{{m}^{2}}\] \[12\sqrt{35}c{{m}^{2}}\]