Question

The cost of turfing a
uniform circular road
around a circular garden at 20 p/m² is 215.60
and the area of garden is 1386m².Find the width
of circular road. ​

Answer 1

Given :-

▪ The cost of turfing a uniform circular road around a circle garden of radius OA at 20 paise/m² is ₹ 215.60 paise.

▪ The area of the garden which is a circle of radius OA is 1386 m²

To Find :-

▪ Width of the road.

Solution :-

Let us find the area of the road given us the rate of turfing the road and total cost.

⇒ Area × Rate = Cost

⇒ Area = 215.60 / 20

⇒ Area = 10.78 m²

Now, Including the road and the garden, we get a circle of radius OB.

But,

⇒ Area of the circle of combined radius = 10.78 + 1386

⇒ Total Area = 1396.78 m²

Let's find OB now,

⇒ πR² = 1396.78

⇒ R² = 444.43

⇒ OB = 21.08 m

Similarly, Let us find OA,

⇒ Area = π(OA)²

⇒ 1386 = (OA)² × 22/7

⇒ OA² = 441

⇒ OA = 21 m

Further,

⇒ Width of road = OB - OA

⇒ Width of road = 21.08 - 21

⇒ Width of road = 0.08 m

Hence, The width of the road is 0.08 m or 8 cm.

Answer 2

Answer:

14m

Step by Step explanation:

Area of turfing = 215.6 ÷ 0.20 = 1078m² (change 20 paise to rupees)

Area of garden = 1386m²

Total area = 1386 + 1078 = 2464m²

Area of inner circle = πr²= 1386

22/7r² = 1386

r² = 1386 X 7/ 22 = 441

r = 21

2464 = π(OB²- OA²)

2464 X 7/22 = OB² - 441

784 = OB² - 441

OB² = 784 +441

OB² = 1225

OB = 35

Hence width of the circular path = 35-21 = 14m