A circular pond is of diameter 43 m is surrounded by a 3 m wide path. find yhe cost of constructing the path at the rate of rs 25 per metre square.
Answers
radius of pond=43/2=21.5m
radius of circular region with Path =21.5+3=24.5m
Area of bigger circular region =3.14×24.5×24.5
=1884.785
Area of pond =1451.465
Path area=1884.785-1451.465=433.32
cost =433.32×25=10833 rupees
Given:
(i) The circular pond has a diameter of 43m
(ii) The path around the pond has a width of 3m
(iii) The cost of constructing the path is at a rate of Rs 25/m.
To find:
(i) The total cost of construction.
Solution:
Given, the diameter of the circular pond is 43m.
Radius = Diameter/2 = 43/2 = 21.5m
We know that for a circle of radius r, its area is given as:
A = Пr²
So, for the pool, its area would be:
A = П(21.5)² m²
Taking П as 3.14, we get the area as
A = 1451.47 m²
As the path is 3m wide, the circular figure formed including the path, will have the radius of (21.5+3)m
= 24.5m
Area = П(24.5)² m²
= 1884.79 m²
So, the area of the path only = (1884.79-1451.47) m²
= 433.32 m²
As 1m² costs Rs 25.
So, 433.32 m² will cost = Rs (25*433.32) m²
= Rs 10833
The total cost of construction is Rs 10833.