A tank with open surface and square base is to contain 500 cubic feet of water find the least cost of lining it with tin at the rate of rs.60per sq. Feet
Answers
Answer:
Rs 18,000
Step-by-step explanation:
Given
A tank with open surface and square base is to contain 500 cubic feet of water find the least cost of lining it with tin at the rate of rs. 60 per sq feet.
.Let the side of base be x and height be h
So x^2 h = 500
h = 500 / x^2
Surface area = x^2 + 4hx
Total cost, C = (x^2 + 4hx) 60
= 60 (x^2 + 2000 / x)
Now dc/dx = 60 (2x – 2000 /x^2)
0 = 60 (2x – 2000 /x^2)
2x – 2000 /x^2 = 0
2x^3 = 2000
x = 10 feet
now least cost will be 60 (10^2 + 2000 /10)
= 60 x 300
= Rs 18,000
Step-by-step explanation:
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