Question

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at 10 per m².

Answer 1

Given:

Road width = 3.5 m

Circumference of inner (circular) plot = 44 m

Rate = 10 per m²

`("Use"  π = 22/7)`

Step-wise calculation:

1. Inner radius

r = `"Circumference"/(2π)` 

= `44/(2 × (22/7)) `

= `44/(44/7)` 

= 7 m

2. Outer radius

R = r + 3.5

= 7 + 3.5

= 10.5 m

3. Area of the road (annulus)

= π(R² – r²) 

= `22/7 [(10.5)^2 - 7^2]` 

= `22/7 [110.25 - 49]` 

= `22/7 (61.25)` 

= 22 × 8.75

= 192.5 m²

4. Cost = Area × Rate

= 192.5 × 10

= 1925

Cost of paving the road = 1925.