A metal box with a square base and vertical sides is to contain 1024 cm3 of water, the material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box.

Explanation

To solve the problem of finding the least cost of a metal box with a square base and vertical sides that can contain 1024 cm³ of water, we will follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = length of the side of the square base (in cm)
- \( y \) = height of the box (in cm)

### Step 2: Volume Constraint
...