Question

Given figure depicts a racing track whose left and right ends are semi-circular. The distance between the two inner parallel line segments is 60 $m$ and they are each 106 $m$ long. If the track is 10 $m$ wide, find the area of the track (in $m^2$).

• A. 4320 $m^2$
• B. 2340 $m^2$
• C. 4320 $m^2$
• D. 5000 $m^2$

Answer 1

The correct option is A 4320 $m^2$

Area of semi-circle = $\frac{1}{2}\times \pi \times r^2$
Area of track = Area of Field - Area inside the track

Area of field
= 106 $\times$ 80 + 2 $\times$ $\frac{1}{2}\times \frac{22}{7}\times {40}^2$
= 13508.57 $m^2$
Area inside the track
= 106 $\times$ 60 + 2 $\times$ $\frac{1}{2}\times \frac{22}{7}\times {30}^2$
= 9188.57 $m^2$
$\therefore$ The area of the track
= 13508.57 - 9188.57
= 4320 $m^2$