lcyaire
02.04.2020 •
Mathematics
A cardboard box without a lid is to have a volume of 23,328 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)
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Ответ:
x,y,z=36cm, 36cm, 18cm
Step-by-step explanation:
Volume of the Cardboard =
The dimensions of the box are x, y and z.
Volume of a Cuboid = xyz.
Since the top is open, there is only one 'xy' side.
Surface Area, f(x,y,z)= xy+2yz+2xz
We take the first derivative of f(x,y)
Equate the derivatives to zero and solve for x and y respectively.
Substituting x into y and vice versa
Recall:
x,y,z=36cm, 36cm, 18cm
Ответ: