Question

A closed box has a square base with side length feet and height feet given that the volume of the box is 34 ft.³ express the surface area of the box in terms of length only

Answer 1

`(2s^3+136)/(s)`

Explanation:

Let the side length of the square base =s feet

Let the height of the box = h

Given that the volume of the box =
`34$ ft^3`

Volume of the box =
`s^2h`

Then:

`s^2h=34$ ft^3\\$Divide both sides by s^2\\h=(34)/(s^2)`

Surface Area of a Rectangular Prism =2(lb+bh+lh)

Since we have a square base, l=b=s feet

Therefore:

Surface Area of our closed box
`= 2(s^2+sh+sh)`

`S$urface Area= 2s^2+4sh\\Recall: h=(34)/(s^2)\\$Surface Area= 2s^2+4s\left((34)/(s^2)\right)\\=2s^2+(136)/(s)\\$Surface Area in terms of length only=(2s^3+136)/(s)`