1. **Stating the problem:** We have two similar tins with masses 2000g and 500g respectively. The area of the base of the smaller tin is 100 square centimeters. We need to find the area of the base of the larger tin. 2. **Understanding similarity and mass relation:** Since the tins are similar, their linear dimensions are proportional. The mass of an object is proportional to its volume, and volume scales as the cube of the linear scale factor. 3. **Calculate the ratio of masses:** $$\text{Mass ratio} = \frac{2000}{500} = 4$$ 4. **Relate mass ratio to linear scale factor:** $$\text{Volume ratio} = \left(\text{linear scale factor}\right)^3 = 4$$ 5. **Find the linear scale factor:** $$\text{linear scale factor} = \sqrt[3]{4}$$ 6. **Relate area of base to linear scale factor:** Area scales as the square of the linear scale factor, so $$\frac{\text{Area of larger base}}{\text{Area of smaller base}} = \left(\text{linear scale factor}\right)^2 = \left(\sqrt[3]{4}\right)^2 = 4^{\frac{2}{3}}$$ 7. **Calculate the area of the larger base:** $$\text{Area of larger base} = 100 \times 4^{\frac{2}{3}}$$ 8. **Simplify the expression:** $$4^{\frac{2}{3}} = \left(2^2\right)^{\frac{2}{3}} = 2^{\frac{4}{3}} = 2^{1 + \frac{1}{3}} = 2 \times 2^{\frac{1}{3}} \approx 2 \times 1.26 = 2.52$$ 9. **Final area:** $$100 \times 2.52 = 252 \text{ square centimeters}$$ **Answer:** The area of the base of the larger tin is approximately 252 square centimeters.