7 metre wide path is to be constructed all around, and outside a circular garden of diameter 112m. find the cost of constructing the path at the rate of Rs. 50 per square metre.

Total Cost of construction =  Rs. 129800

Step-by-step explanation:

To find the cost of construction, lets find the area of the path first.

Garden Diameter Dg = 112 m

As the path is 7 m wide, and outside of the garden,

Diameter of the outside perifery of the path Dp = 112 +7+7

∴ Dp = 126 m

Area of the path = Area of outside circle of the path - Area of the garden

∴ Ap = (π/4) Dp² - (π/4) Dg²

∴ Ap = (π/4) × (Dp² - Dg²)

Substituting the values, we get,

Ap = [(22/7)/4] × (126² - 112²)

∴ Ap = (11/14) × (126+112)×(126-112)

∴ Ap = (11/14) × 236 × 14

∴ Ap = 11 × 236

∴ Ap = 2596 m²

∴ Area of the path = 2596 m²

Cost of cunstruction is Rs.50 per m²

∴ Total Cost = Cost of construction × Area of the path

∴ Total Cost = 50 × 2596

∴ Total Cost = 129800 Rs

Total Cost of construction =  Rs. 129800

Step-by-step explanation: