A 7 m wide path is to be constructed all around and outside a circular
garden of diameter 112 m. Find:
a) the area of the garden.
b) area of the garden along with the path.
c) area of the path.
d) the cost of constructing the path at 20 per m2.
Answers
Step-by-step explanation:
Radius of the circular garden, r=
2
210
=105m
Radius of the region covering the garden and the path, R=105m+7m=112m
Area of the region between two concentric circles
with radius of outer circle R, and inner circle r =π(R
2
−r
2
)
Hence, the area of the path =π(112
2
−105
2
)=
7
22
(12544−11025)=
7
33418
=4774m
2
Total Cost of construction = Rs. 129800
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.20 per m²
∴ Total Cost = Cost of construction × Area of the path
∴ Total Cost = 20 × 2596
∴ Total Cost = 51 920 Rs
Total Cost of construction
☆=> ₹51920☆