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

5,391.76

Explanation:

Answer 2

The length of the track is 247 m.

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

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 (
`(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 (
`(\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.