Respuesta :
Answer:
Step-by-step explanation:
Given
Volume of box [tex]V=32,000 cm^3[/tex]
Let b be the square base and h be the height of box
Volume [tex]V=b^2\cdot h[/tex]
[tex]h=\frac{V}{b^2}[/tex]
Surface Area [tex]A=b^2+4bh [/tex]
[tex]A=b^2+4b\times \frac{V}{b^2}[/tex]
[tex]A=b^2+4\frac{V}{b}[/tex]
Differentiate A w.r.t b to get maxima/minima
[tex]\frac{\mathrm{d} A}{\mathrm{d} b}=2b-\frac{4\times V}{b^2}[/tex]
[tex]2b-\frac{4\times V}{b^2}=0[/tex]
[tex]b^3=\frac{4V}{2}[/tex]
[tex]b^3=\frac{4\times 32,000}{2}[/tex]
[tex]b=40 cm[/tex]
[tex][tex]h=\frac{32,000}{40\times 40}[/tex]
[tex]h=20 cm[/tex]
