school ground is in the shape of a circle with
radius 103 m. Four tracks each of 3 m wide has to be
constructed inside the ground for the purpose of
track events. Find the cost of constructing the track
at the rate of ₹50 per sq.m.
Answers
Answer:
Track A = Rs. 95700
Track B = Rs. 92872
Track C = Rs. 90043
Track D = Rs. 87215
Step-by-step explanation:
Given that each of the four tracks is 3 m wide.
• To find the cost of construction for track A:
The radius of the circular ground is 103 m
Then the radius of the ground except track A be (103 - 3) m = 100 m
So the area of track A be
= π (103² - 100²) m²
= 22/7 * 609 m²
= 1914 m²
Therefore the cost of construction for track A is
= Rs. (50 * 1914)
= Rs. 95700
• To find the cost of construction for track B:
The radius of the circular ground except track A is (103 - 3) m = 100 m
Then the radius of the ground except track A and track B be {103 - (3 * 2)} m = 97 m
So the area of track B be
= π (100² - 97²) m²
= 22/7 * 591 m²
= 13002/7 m²
Therefore the cost of construction for track B is
= Rs. (50 * 13002/7)
= Rs. 92872
• To find the cost of construction for track C:
The radius of the circular ground except track A and track B is {103 - (3 * 2)} m = 97 m
Then the radius of the ground except track A, track B and track C be {103 - (3 * 3)} m = 94 m
So the area of track C be
= π (97² - 94²) m²
= 22/7 * 573 m²
= 12606/7 m²
Therefore the cost of construction for track C is
= Rs. (50 * 12606/7)
= Rs. 90043
• To find the cost of construction for track D:
The radius of the circular ground except track A, track B and track C is {103 - (3 * 3)} m = 94 m
Then the radius of the ground except the four tracks be {103 - (3 * 4)} m = 91 m
So the area of track D be
= π (94² - 91²) m²
= 22/7 * 555 m²
= 12210/7 m²
Therefore the cost of construction for track D is
= Rs. (50 * 12210/7)
= Rs. 87215
•• To find the total cost of construction for four tracks:
Given that the radius of the circular ground is 103 m. Then the radius of the ground except the four tracks is {103 - (4 * 3)} m = 91 m.
Then the area of the four tracks is
= π (103² - 91²) m²
= 22/7 * 2328 m²
= 51216/7 m²
Therefore the cost of construction for four tracks is
= Rs. (50 * 51216/7)
= Rs. 365829
Answer:
Step-by-step explanation:
Inner radius (r)=91 m
Outer radius (R)=103 m
Area of circular path =π(R2-r2) sq units
22/7 ((103)2-(91)2)
22/7*(10609-8281)
22/7*2328
7316.5714 sq m
Cost of constructing the track is=₹50 per sq.m
.°. total cost =7316.5714*50
=₹365828.57