Mathematics
candy6420
2016-04-10 08:53:36
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 64cm^2
ANSWERS
Fitsgerald261
2016-04-10 10:01:47

Let x =lenght, y = width, and z =height  The volume of the box is equal to V = xyz  Subject to the surface area  S = 2xy + 2xz + 2yz = 64  = 2(xy + xz + yz)  = 2[xy + x(64/xy) + y(64/xy)]  S(x,y)= 2(xy + 64/y + 64/x)  Then  Mx(x, y) = y = 64/x^2  My(x, y) = x = 64/y^2  y^2 = 64/x  (64/x^2)^2 = 64  4096/x^4 = 64/x  x^3 = 4096/64  x^3 = 64  x = 4  y = 64/x^2  y = 4  z= 64/yx  z= 64/16  z = 4  Therefor the dimensions are cube 4.

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