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Diagram 5 shows a piece of rectangular cardboard. An open box is formed from the cardboard by cutting out four spaces of equal size from every corner and then bending up the sides. Find the sides of the square to be cut out in order to get a box with largest volume

Diagram 5 shows a piece of rectangular cardboard An open box is formed from the cardboard by cutting out four spaces of equal size from every corner and then be class=


Answer :

Answer:

The highest side to be cut out is 10/3 cm

Explanation:

Let the size of the square be s, then the volume of the box is:

s(15 - 2s)(40 - 2s). This can be written as:

[tex]4s^3-110s^2+600s[/tex]

Taking the derivative, we have:

[tex]12s^2-220s+600[/tex]

Set the above = 0, and take the roots:

[tex]\begin{gathered} 12s^2-200s+600=0 \\ s=\frac{10}{3} \\ \\ OR \\ s=15 \end{gathered}[/tex]

s = 15 is not practical, so we use s = 10/3

The maximum volume is therefore;

[tex]\begin{gathered} (\frac{10}{3})(15-\frac{20}{3})(40-\frac{20}{3}) \\ \\ =925.925\operatorname{cm}^3 \end{gathered}[/tex]

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