# A closed box has a square base with side length l feet and height h feet. Given that the volume of the box is 35 cubic feet, express the surface area of the box in terms of l only. ??

Aug 23, 2017

$A = \frac{2 \left(70 + {I}^{3}\right)}{I}$

#### Explanation:

So we are told that the box has a square base, so all four sides are the same length I.

Volume = Length x Breadth x Height

So we know that Length and Breadth are both equal to I. Hence

$35 = I \cdot I \cdot h$

$\implies h = \frac{35}{I} ^ 2$

Now we need to calculate the surface are of the box. There are four side faces with area $I \cdot h$ as well as a top and bottom face of area ${I}^{2}$. Therefore

$A = 4 \left(I \cdot h\right) + 2 {I}^{2}$

$A = 4 I \cdot \frac{35}{I} ^ 2 + 2 {I}^{2}$

$A = \frac{140}{I} + 2 {I}^{2}$

$A = \frac{2 \left(70 + {I}^{3}\right)}{I}$