Question

An oval track is made by erecting semicircles on each end of a 46 m by 92 m rectangle. Find the length of the track and
the area enclosed by the track.

Answer 1

Answer:

$Length\,\, of\,\, the\,\, track=420.44\,m\\\\Area\,\,covered \,\,by\,\, the\,\, track=5893.06\,m^2$

Step-by-step explanation:

Length of the Track:

Perimeter of the rectangle + Circumference of the two semicircle

Perimeter of the rectangle= $2(Length+Width)$

$Length=92\,m\\Width=46\,m$

Perimeter of the rectangle:

              $=2(92+46)\\\\=2(138)\\\\=276\,m$

Circumference of Two Semicircle with same radius:

$r=\dfrac{46}{2} =23\,m$

$Circumference=2\times \pi \times r$

   $=2\times 3.14\times 23\\\\=6.28 \times 23\\\\=144.44\,m$

Total Length of the track is :

$=276+144.44\\\\=420.44\,m$

Area Covered by the track is :

Area of the two semicircle + Area of the rectangle

         $=(\pi \times r^2) + (Length\times Width)\\\\=(3.14\times (23\times 23 ))+(92\times 46)\\\\=1661.06 +4232\\\\=5893.06\,m^2$