Find the dimensions of the largest open-top storage bin with a square base and v

Question

Find the dimensions of the largest open-top storage bin with a square base and vertical sides that can be made from 108 ft^2 of sheet steel. (neglect thickness of steel)

Explanation / Answer

Assume base width is w and height is h. So base area is w*w. Area of each side is w*h. So total area of steel used is w*w + 4*w*h Now we know this area is 108, => w*w + 4*w*h = 108 => 4wh = 108 - w^2 => h = 27/w - w/4 volume v = w*w*h = w*w*(27/w - w/4) = 27w - w^3/4 Now imagine a plot of w versus v. The maximum v will be at the peak of this plot, which will be when the slope is 0, i.e. when dv/dw = 0. So take the deriviative, and where that is 0, that will give you the w for maximum v. Then you can work out the dimensions from there.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.