Question

A uniform circular track is the area bounded by two concentric circles . if the area of the track is 114 metre square and its width is 14 m ;find the diameter of two circles​

Answer 1

Answer:

Diameter of large circle is 39.4 m and diameter of small circle is 11.4 m .

Step-by-step explanation:

Let A be the area of the larger circle with radius R.

Let a be the area of the smaller circle with radius r.

Here we are given that width of the track is 14m.

Width of track = R - r

14 = R - r

R = 14 + r

Area of the track = A - a

114 = πR² - πr²

114 = π ( R² - r² )

114 = π [ (14 + r )² - r² ]

114 = π ( 196 + 28r + r² - r² )

114 = π ( 196 + 28r )

114 = 3.14 ( 196 + 28r )

114 = 615.44 + 87.92r

501.44 = 87.92r

r = 5.7 m

The diameter of large circle = (r+14) x 2

= 39.4 m

The diameter of small circle = r x 2

= 11.4 m