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Tcecarenko [31]
3 years ago
13

An open-topped glass aquarium with a square base is designed to hold 13.513.513, point, 5 cubic feet of water. what is the minim

um exterior surface area of the aquarium?
Mathematics
1 answer:
ExtremeBDS [4]3 years ago
3 0
Suppose the aquarium's shape is a square prism, with each side of the square having length x, and the aquarium's height is y, so we have: 
<span> x^2 * y = 13.5
</span> <span>y = 13.5/(x^2) 
</span><span> The area of each side is xy, and there are four sides, so that totals 4xy 
</span><span> The area of the bottom is x^2 
</span><span> Total surface area: 
</span><span> A = x^2 + 4xy 
</span><span> A = x^2 + 4x(13.5/(x^2))
</span> <span>A = x^2 + 54x^(-1) 
</span><span> dA/dx = 2x - 54x^(-2) 
</span><span> Set the derivative to zero: 
</span><span> 2x - 54x^(-2) = 0 
</span><span> 2x = 54/(x^2) 
</span><span> 2x^3 = 54 
</span><span> x^3 = 54/2 
</span><span> x^3 = 27 
</span><span> x = cbrt(27) = 3, assuming x is a real number 
</span><span> A = 3^2 + 54*3^(-1) 
</span><span> A = 9 + 18
</span><span> A = 27 square feet</span>
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