Question

A park is in the form of a rectangle 100 m × 80 m. At the centre of the park there is a circular lawn. The area of the park excluding the lawn is 4150 m². Find the radius of the circular lawn.

Answer 1

Given: Rectangle park 100 m × 80 m; area of park excluding the circular lawn = 4150 m².

Step-wise calculation:

1. Area of the rectangular park.

= 100 × 80

= 8000 m²

2. Area of the circular lawn.

= Total area – Area excluding lawn

= 8000 – 4150

= 3850 m²

3. Let r be the radius of the circular lawn.

Area of circle = πr²

= 3850

So, `r^2 = 3850/π`

4. `r = sqrt(3850/π)`

= `sqrt(3850/3.141592653589793...)`

= `sqrt(1225.493)`

= 35.01 m

Radius of the circular lawn

= `sqrt(3850/π) m`

= 35.01 m   ...(Approximately 35.0 m)