Block-shaped 7976

A block-shaped pool with a volume of 200m3 is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m2 of the pool bottom is 2 times cheaper than 1 m2 of the pool wall. What dimensions must the pool have to make the construction the cheapest?

Correct answer:

a =  20 m
b =  5 m
c =  2 m

Step-by-step explanation:

V=200 m3 a = 4b  p = ab/2 + 2(a+b) c V = abc 200 = 4b2 c  c = 50 / b2  p = 4b2/2 + 2(4b+b) 50 / b2 p = 2b2 + 500b / b2 p = 2b2 + 500 / b  p = 4b  500/b2 p=0  4b3=500 b=3500/4=5 m a=4 b=4 5=20 m
b=5=5 m
c=50/b2=50/52=2 m

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