The radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levelling it at Rs. 20 per m^{2}. [Use π = 3.14.]

Here we will first find out the area of the road running around the circular garden and then multiplying it with rate per square meter to calculate the cost of leveling.

Here we see in the figure there are two concentric circles so,

Area of road = Area of outer circle- Area of circular garden

Area of circle = πR^{2} (where R = radius of circle) → eqn1

Let the radius of inner circle = r = 100 m

Also, radius of outer circle = R = 110 m (R = r + 10)

Area of outer circle = π(110)^{2}→ eqn2 (putting R in eqn1)

Area of inner circle = π(100)^{2}→ eqn2 (putting r in eqn1)

∴ Area of road = π(110)^{2} – π(100)^{2} (from eqn2 and 3)

⇒ Area of road = π(12100 – 10000)

⇒ Area of road = 2100 π (put π = 3.14)

⇒ Area of road = 2100×3.14

∴ Area of road = 6594 m^{2}

Cost of leveling = Rate of leveling × Area of road

⇒ Cost of leveling = 20×6594

∴ Cost of leveling = Rs.131880

Area of road is 6594 m^{2} and cost of leveling is Rs.131880.

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