A student survey was conducted at a major university. Data were collected from a random sample of 206 undergraduate students, an
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Answer:
The volume of the box is maximized when x = 0.53 cm
Therefore, x = 0.53 cm and the Maximum volume = 1.75 cm³
Step-by-step explanation:
Please refer to the attached diagram:
The volume of the box is given by
Let x denotes the length of the sides of the square as shown in the diagram.
The width of shaded region is given by
The length of shaded region is given by
So, the volume of the box becomes,
Take the derivative of volume and set it to zero.
We may solve the quadratic equation using the quadratic formula.
The values of coefficients a, b, c are
Substituting the values into quadratic formula yields,
Volume of box when x = 1.59:
Volume of box when x = 0.53:
As you can see, the volume of the box is maximized when x = 0.53 cm
Therefore, x = 0.53 cm and the Maximum volume = 1.75 cm³
