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 m2. [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 = πR2 (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 m2
Cost of leveling = Rate of leveling × Area of road
⇒ Cost of leveling = 20×6594
∴ Cost of leveling = Rs.131880
Area of road is 6594 m2 and cost of leveling is Rs.131880.