If 10,800 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
(first use surface area equation \(\displaystyle x^{2} + 4xy = \)Surface area, then use Volume equation \(\displaystyle l * w * h\) or \(\displaystyle x^{2}y\) and then back to surface area equation after doing the derivative on the volume equation)
\(\displaystyle x^{2} + 4xy = \)Surface area
\(\displaystyle x^{2} + 4xy = 10,800\)
\(\displaystyle \dfrac{x^{2}}{4x} + \dfrac{4xy}{4x} = \dfrac{10,800}{4x}\)
\(\displaystyle \dfrac{x^{2}}{4x} + y = \dfrac{10,800}{4x}\)
\(\displaystyle y = \dfrac{10,800}{4x} - \dfrac{x^{2}}{4x} \) On the right track here?
(first use surface area equation \(\displaystyle x^{2} + 4xy = \)Surface area, then use Volume equation \(\displaystyle l * w * h\) or \(\displaystyle x^{2}y\) and then back to surface area equation after doing the derivative on the volume equation)
\(\displaystyle x^{2} + 4xy = \)Surface area
\(\displaystyle x^{2} + 4xy = 10,800\)
\(\displaystyle \dfrac{x^{2}}{4x} + \dfrac{4xy}{4x} = \dfrac{10,800}{4x}\)
\(\displaystyle \dfrac{x^{2}}{4x} + y = \dfrac{10,800}{4x}\)
\(\displaystyle y = \dfrac{10,800}{4x} - \dfrac{x^{2}}{4x} \) On the right track here?