The area of a circular playground is 154 metre² a path of width 2m is laid around and outside of it find the cost of levelling the path at the rate of 7 per square metre
Answers
Answer :
The cost of levelling the path = Rs. 703.99
Given :
- Area of circular playground = 154 m²
- Width of a path which is laid around and outside the circular ground = 2 m
- Rate of levelling the path = Rs. 7
To find :
- Cost of levelling the whole path
Solution :
Using formula,
- Area of circle = πr²
where,
- Take π = 22/7
- r denotes the radius of the circle
Substituting the given values :
⇒ 154 = πr²
⇒ 154 = 22/7 × r²
⇒ 154 × 7/22 = r²
⇒ 77 × 7/11 = r²
⇒ 7 × 7 = r²
⇒ 49 = r²
⇒ Taking square root on both sides :
⇒ √49 = r
⇒ ± 7 Reject -ve = r
⇒ 7 = r
- Radius of the circular playground = 7 m
Calculating the radius of the circular playground + path :
⇒ Radius of circular playground + Width of path
⇒ 7 + 2
⇒ 9
- Radius of the circular playground + path = 9 m
Using formula,
- Area of circle = πr²
Substituting the given values :
⇒ Area = 22/7 × (9)²
⇒ Area = 22/7 × 81
⇒ Area = 1782/7
⇒ Area = 254.57
- Area of the circular playground + path = 254.57 m²
⇒ Area of the path = Area of circular playground + path - Area of circular playground
⇒ Area of the path = 254.57 - 154
⇒ Area of the path = 100.57
- Area of the path = 100.57 m²
⇒ Cost of levelling the path = Area of the path × Rate of levelling the path
⇒ Cost of levelling the path = 100.57 × 7
⇒ Cost of levelling the path = 703.99
Therefore,
- The cost of levelling the path = Rs. 703.99