2. A closed box has a square base with side length $l$ feet and height $h$ feet. Given that the volume of the box is 17 cubic feet, express the surface area of the box in terms of $l$ only.
Answer
Final Answer: The surface area of the box in terms of $l$ only is \(\boxed{2l^2 + \frac{68}{l}}\).
Step 1 ：Given that the volume of a box with a square base and height $h$ is 17 cubic feet, we can express this as $l^2h = 17$.
Step 2 ：Solving this equation for $h$, we get $h = \frac{17}{l^2}$.
Step 3 ：The surface area of a box with a square base is given by the formula $A = 2l^2 + 4lh$.
Step 4 ：Substituting $h = \frac{17}{l^2}$ into the surface area formula, we get $A = 2l^2 + \frac{68}{l}$.
Step 5 ：Final Answer: The surface area of the box in terms of $l$ only is \(\boxed{2l^2 + \frac{68}{l}}\).
