1. **State the problem:** We have two similar tanks with capacities 1,000,000 litres and 512,000 litres respectively. The smaller tank has a surface area of 1200 m². We need to find the difference in their surface areas. 2. **Understand similarity and scaling:** For similar shapes, volumes scale as the cube of the linear scale factor $k$, and surface areas scale as the square of $k$. 3. **Find the volume scale factor:** Let $V_1 = 1,000,000$ litres and $V_2 = 512,000$ litres. The scale factor for volume is: $$k^3 = \frac{V_1}{V_2} = \frac{1,000,000}{512,000} = \frac{125}{64}$$ 4. **Find the linear scale factor $k$:** $$k = \sqrt[3]{\frac{125}{64}} = \frac{5}{4} = 1.25$$ 5. **Find the surface area scale factor:** Surface areas scale as $k^2$: $$k^2 = \left(\frac{5}{4}\right)^2 = \frac{25}{16} = 1.5625$$ 6. **Calculate the larger tank's surface area:** Given the smaller tank's surface area $S_2 = 1200$ m², $$S_1 = k^2 \times S_2 = 1.5625 \times 1200 = 1875 \text{ m}^2$$ 7. **Find the difference in surface areas:** $$\text{Difference} = S_1 - S_2 = 1875 - 1200 = 675 \text{ m}^2$$ **Final answer:** The difference in surface areas is $675$ m².