Respuesta :
The largest possible volume of the box is 6158.394 cm^3.
Define the dimensions of the box to be L, W, and H.
Square base, L = W
Area: A = L^2 * H
Surface Area (Base + Area of 4 sides):
1600 = L^2 + 4 (L*H) ⇒ H = (1600 - L^2) / (4L)
Area: A = 400L - (1/4)L^3
Maximum (Derivative) A' = 400 - (3/4)L^2
Solving for 0
0 = 400 - (3/4)L^2
L^2 ⇒ (40 * SQRT(3)) / 3 = 23.094 (Maximum)
Solving for dimensions, known L=23.094
L = 23.094 cm
W = 23.094 cm
H ⇒ (1600 - L^2) / (4L) = (20 * SQRT(3) / 3) = 11.547 cm
Volume ⇒ L*W*H = 6158.394 cm^3
To locate the most viable extent, add the greatest viable mistakes to every dimension, then multiply. To find the minimum viable volume, subtract the greatest feasible mistakes from each measurement, then multiply.
Volume is a scalar amount expressing the amount of 3-dimensional area enclosed by a closed surface. For example, the gap that a substance or 3-D shape occupies or consists of.
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