1. **Problem statement:** We need to show that the surface area $O(a)$ of a box with a square base of side length $a$ and volume 300 ml (or 300 cm³) can be described by the function $$O(a) = 2a^2 + \frac{1200}{a}.$$ 2. **Given:** - Volume $V = 300$ ml = 300 cm³ - Base is square with side length $a$ - Height $h$ unknown 3. **Step 1: Express height $h$ in terms of $a$ using volume formula** Volume of a box with square base: $$V = a^2 \times h$$ Given $V=300$, so: $$300 = a^2 h \implies h = \frac{300}{a^2}$$ 4. **Step 2: Write the surface area formula** Surface area $O$ consists of: - Two square bases: $2 \times a^2$ - Four rectangular sides: each side $a \times h$, total $4ah$ So: $$O = 2a^2 + 4ah$$ 5. **Step 3: Substitute $h$ from step 3 into surface area formula** $$O = 2a^2 + 4a \times \frac{300}{a^2} = 2a^2 + \frac{1200}{a}$$ 6. **Conclusion:** We have shown that the surface area $O$ as a function of $a$ is: $$O(a) = 2a^2 + \frac{1200}{a}$$ This matches the given function, so the statement is proven.