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

Answer:

$\dfrac{2s^3+136}{s}$

Step-by-step 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:

$s^2h=34 ft^3\\ Divide both sides by s^2\\h=\dfrac{34}{s^2}$

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$= 2(s^2+sh+sh)$

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