Question

A 7m wide road surrounds a circular garden whose area is 5544m². Find the area of the road and the cost of tarring it at the rate of Rs.150 per m².

Answer 1

we know,

The area of the ring between two concentric circles equals the area of the larger circle minus the area of smaller circle.
Let the radius of the outer and inner ring be R and r respectively.
Here the circular garden is the inner circle and the 7m wide road os the ring area of the ring between two concentric circles = π(R² - r²)
The Area of a Circle with radius r = πr2
Here, 
πr² = 5544m²
⇒ r = 42
⇒ R = 42 + 7
= 49
inner Circle has radius r 
= 42 and outer Circle has radius R
= 49
π(49² - 42²⁾

= `(22)/(7) xx (2401 - 1764)`

= `(22)/(7) xx 637`
= 2002m²
The cost of paying the road at the rate of Rs.150per m²
= 2002 x 150
= Rs.3,00,300.