Her 7 metre wide path is to be constructed all around and outside a circular garden of diameter 112 m find the cost of construction 50 rupees per square metre
Answers
Answer:
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
Answer:
Rs 130900
Step-by-step explanation:
Her 7 metre wide path is to be constructed all around and outside a circular garden of diameter 112 m find the cost of construction 50 rupees per square metre
Diameter of Garden = 112 m
Radius of Garden = 112/2 = 56 m
Wide path around circle = 7 m
Radius of garden + path = 56 + 7 = 63 m
area of Path = Area of (garden + path) - Area of Garden
= π 63² - π 56²
= (22/7)(63 × 63) - (22/7)(56×56)
= 22(63 × 9 - 56×8)
= 22(567 - 448)
= 22(119)
= 2618 m²
Cost Per meter = Rs 50
Total Cost = 2618 * 50 = Rs 130900