Anish investigated the effect of the surface-area-to-volume ratio of plant tissue on the rate of osmosis. He cut three different-sized cubes of fresh cucumber with side lengths of 1.5 cm, 3.0 cm, and 4.5 cm. He recorded their original masses, immersed them in a beaker of deionised water for 90 minutes, and then recorded their final masses.
The table below shows his results:
| Cucumber cube size in cm | Original mass in g | Final mass in g | Percentage change in mass (%) |
|---|---|---|---|
| 1.5×1.5×1.51.5 \times 1.5 \times 1.51.5×1.5×1.5 | 3.24 | 3.82 | 17.90 |
| 3.0×3.0×3.03.0 \times 3.0 \times 3.03.0×3.0×3.0 | 25.92 | 28.15 | |
| 4.5×4.5×4.54.5 \times 4.5 \times 4.54.5×4.5×4.5 | 87.48 | 91.20 | 4.25 |
Calculate the percentage change in mass for the 3.0×3.0×3.0 cm3.0 \times 3.0 \times 3.0\text{ cm}3.0×3.0×3.0 cm cucumber cube. Show your working and give your answer to two decimal places.
Calculate the surface area (SA), volume (Vol), and SA:Vol ratio for the 4.5×4.5×4.5 cm4.5 \times 4.5 \times 4.5\text{ cm}4.5×4.5×4.5 cm cucumber cube using the following formulae:
SA=6×(side length in cm)2\text{SA} = 6 \times (\text{side length in cm})^2SA=6×(side length in cm)2 Vol=(side length in cm)3\text{Vol} = (\text{side length in cm})^3Vol=(side length in cm)3