1. **Problem statement:** We have a cylindrical beaker with radius 4 cm and height 12 cm. We need to find its volume, then calculate the volumes of acid and water when filled with a 5% acid solution, and finally find how much solution is needed to get exactly 35 cm³ of acid. 2. **Formula for volume of a cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the volume of the beaker:** $$V = \pi (4)^2 (12) = 192\pi \text{ cm}^3$$ Approximating $\pi \approx 3.1416$: $$V \approx 192 \times 3.1416 = 603.19 \text{ cm}^3$$ Rounded to nearest cm³: $$V = 603 \text{ cm}^3$$ 4. **Calculate volume of acid and water when beaker is full:** The solution is 5% acid, so acid volume is: $$603 \times 0.05 = 30.15 \text{ cm}^3$$ Water volume is total minus acid: $$603 - 30.15 = 572.85 \text{ cm}^3$$ Rounded to nearest cm³: Acid = 30 cm³, Water = 573 cm³ 5. **Calculate volume of solution needed for 35 cm³ acid:** Since 5% of solution is acid, let $x$ be volume of solution: $$0.05x = 35$$ Divide both sides by 0.05: $$x = \frac{35}{0.05}$$ Show cancellation: $$x = \frac{35}{\cancel{0.05}} \times \cancel{\frac{1}{0.05}} = 700 \text{ cm}^3$$ 6. **Calculate volumes of acid and water in 700 cm³ solution:** Acid volume: $$700 \times 0.05 = 35 \text{ cm}^3$$ Water volume: $$700 - 35 = 665 \text{ cm}^3$$ **Final answers:** - Volume of beaker: 603 cm³ - Volume of acid in full beaker: 30 cm³ - Volume of water in full beaker: 573 cm³ - Volume of solution needed for 35 cm³ acid: 700 cm³ - Corresponding water volume: 665 cm³ Your calculations are correct except for minor rounding differences in the volumes of acid and water in the beaker (30.15 and 572.85 rounded to 30 and 573 respectively).