Question

An oval track is made by erecting semicircles on each end of a 44 m by 88 m rectangle. Find the length of the track and the area enclosed by the track.

Answer 1

Answer:

The length of the track is 247 m.

The area enclosed by the track is  5391 . 76 sq m.

Step-by-step explanation:

The length of the rectangle  = 88 m

The width of the rectangle  =  44 m

Now, as we know the semicircles are at the end of rectangular track.

So, the diameter of semicircles = Width of the rectangle

⇒ The diameter of the semi circle  = 44 m

⇒Radius of the semi circle  = 44/2 = 22 m

TOTAL LENGTH OF TRACK  

= 2 ( Length of rectangle)  + 2 (Circumference of 1 semicircle)

= 2 x (88 m)  + 2 ($\frac{2\pi r}{2}$)

= 176 m + 2 (3.14)(22 m)  = 176 + 71.08 =  247 m

Hence, the length of the track is 247 m

TOTAL AREA OF TRACK  

= (Area of rectangle)  + 2 (Area of 1 semicircle)

= (Length x Width)  +    2 ($\frac{\pi r^2}{2}$)

=  (44  m x 88 m) +  (3.14)(22 m)(22 m)   = (3872  + 1519.76) sq m

=  5391 . 76 sq m

Hence, the area enclosed by the track is  5391 . 76 sq m.