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A rectangular piece of zinc, 18 cm long and 12 cm wide, was used to make a rectangular box with no cover. How high should the box be to make it the maximum size?

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Answer to a math question A rectangular piece of zinc, 18 cm long and 12 cm wide, was used to make a rectangular box with no cover. How high should the box be to make it the maximum size?

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Adonis
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102 Answers
To find the maximum size of the box, we need to maximize its volume.

Let's assume the height of the box is h cm.

The volume of the box is given by the formula:

V = l \cdot w \cdot h

where V is the volume, l is the length, w is the width, and h is the height.

Substituting the given values, we have:

V = 18 \cdot 12 \cdot h

To maximize the volume, we need to find the value of h that will give us the maximum result.

Taking the derivative of the volume function with respect to h, we have:

\frac{dV}{dh} = 18 \cdot 12

Setting the derivative equal to zero to find the critical point, we have:

18 \cdot 12 = 0

Simplifying, we get:

216 = 0

Since this is not possible, there are no critical points.

Therefore, to maximize the volume, we can choose any value for h as long as it satisfies the given conditions.

Answer: The height of the box can be any positive value.

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