(B) Find the dimensions of a box with a square base with surface area 44 and the maximal Volume. Cuse Symbolic notation and fractions where needed.) Side of base: ? : Height ? maximum volume: Here are some information that could be helpful : Becall the formulas for the volume and the surface armo of a box with a square base. V = x² n S = 2x² + 4xh using the formuld for the volume, rewrite the surface area function in terms of X only, S (X). Find the extremum of the surface area.

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Author:James Stewart
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Chapter1: Functions And Models
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hello please answer this calculus question attached below

### Problem: Finding Dimensions of a Box 

Find the dimensions of a box with a square base with surface area 44 and the maximal volume.
*(Use symbolic notation and fractions where needed.)*

- **Side of base:** ?
- **Height:** ?
- **Maximum volume:** ?

### Additional Information

Here are some pieces of information that could be helpful:

Recall the formulas for the volume and the surface area of a box with a square base:

\[ V = x^2 h \]

\[ S = 2x^2 + 4xh \]

Using the formula for the volume, rewrite the surface area function in terms of \( x \) only, \( S(x) \). Find the extremum of the surface area.
Transcribed Image Text:### Problem: Finding Dimensions of a Box Find the dimensions of a box with a square base with surface area 44 and the maximal volume. *(Use symbolic notation and fractions where needed.)* - **Side of base:** ? - **Height:** ? - **Maximum volume:** ? ### Additional Information Here are some pieces of information that could be helpful: Recall the formulas for the volume and the surface area of a box with a square base: \[ V = x^2 h \] \[ S = 2x^2 + 4xh \] Using the formula for the volume, rewrite the surface area function in terms of \( x \) only, \( S(x) \). Find the extremum of the surface area.
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