1. **Problem 4.2:** Church members claim that if they buy 5 litre tins, the number of tins will be three times the number of 20 litre tins. 2. Let the number of 20 litre tins be $x$. 3. Total paint volume from 20 litre tins = $20x$ litres. 4. To cover the same area, the total paint volume from 5 litre tins must also be $20x$ litres. 5. Number of 5 litre tins needed = $\frac{20x}{5} = 4x$. 6. The claim is that the number of 5 litre tins is $3x$, but calculation shows it is $4x$. 7. Therefore, the claim is **not valid** because $4x \neq 3x$. 8. **Problem 4.3:** Verify if Box A can pack two times more 5 litre tins than Box B. 9. Calculate volume of Box A: $$V_A = 140 \times 105 \times 30 = 441000 \text{ cm}^3$$ 10. Calculate volume of Box B: $$V_B = 72 \times 55 \times 50 = 198000 \text{ cm}^3$$ 11. Calculate volume of one 5 litre tin (cylinder): Radius $r = 11$ cm, height $h = 28$ cm. $$V_{tin} = \pi r^2 h = \pi \times 11^2 \times 28 = \pi \times 121 \times 28 = 3388\pi \approx 10644.0 \text{ cm}^3$$ 12. Number of tins in Box A: $$n_A = \frac{V_A}{V_{tin}} = \frac{441000}{10644} \approx 41.4$$ 13. Number of tins in Box B: $$n_B = \frac{V_B}{V_{tin}} = \frac{198000}{10644} \approx 18.6$$ 14. Ratio of tins packed in Box A to Box B: $$\frac{n_A}{n_B} = \frac{41.4}{18.6} \approx 2.23$$ 15. Since $2.23 > 2$, Box A can pack more than twice the number of tins as Box B. 16. Therefore, the packers' argument is **valid**. **Final answers:** - 4.2: The claim is not valid. - 4.3: The claim is valid.