A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹50 per m².

Let the radius of circular plot = R meters.

Given,

Circumference of circular plot = 44 m

2πR = 44

$\Rightarrow 2 \times \dfrac{22}{7} \times R = 44 \\[1em] \Rightarrow R = \dfrac{44 \times 7}{2 \times 22} \\[1em] \Rightarrow R = 7 \text{ m}.$

From figure,

Radius of outer circle = 7 + 3.5 = 10.5 m.

Area of road = Area of outer circle - Area of inner circle

= π(10.5)² - π(7)²

= 110.25π - 49π

= 61.25π

= $\dfrac{22}{7} \times 61.25$

= 192.5 m².

Cost of paving road = Area of road × Rate of paving the road

= 192.5 × 50

= ₹9625.

Hence, cost of paving the road = ₹9625.