Which volume-to-surface-area ratio would be better for an ice cube— the lowest possible or the highest possible? Use the table to help you try different shapes and sizes to make your selection (You can show your work on a separate piece of paper.):
The highest possible volume-to-surface-area ratio would be better for an ice cube. This is because a higher ratio means that the ice cube has a larger volume relative to its surface area, which means that it will take longer for the ice cube to melt. To find the highest possible ratio, we can look at the table and compare the different shapes and sizes. For example, a cube with a side length of 2 cm has a volume of 8 cm3 and a surface area of 24 cm2, giving it a ratio of 8/24 = 0.33. A sphere with a radius of 1 cm has a volume of 4.19 cm3 and a surface area of 12.57 cm2, giving it a ratio of 4.19/12.57 = 0.33. Therefore, the cube and the sphere have the same ratio, and the highest possible ratio is 0.33.
To determine which volume-to-surface-area ratio would be better for an ice cube, let's analyze the options.
The volume-to-surface-area ratio can be calculated by dividing the volume of the ice cube by its surface area. The volume measures the amount of space inside the ice cube, while the surface area measures the exposed area of the ice cube.
Generally, ice cubes with a higher volume-to-surface-area ratio take longer to melt because their volume is larger compared to their surface area. Therefore, to minimize melting, the lowest possible volume-to-surface-area ratio would be preferred.
We can apply this concept to different shapes and sizes of ice cubes to see the effect on their volume-to-surface-area ratios. For instance, if we compare a smaller ice cube with a larger ice cube of the same shape, the larger one will have a lower volume-to-surface-area ratio.
Similarly, comparing different shapes, we can use the table to calculate the volume and surface area for different shapes and sizes of ice cubes, and then compute their respective volume-to-surface-area ratios. We can compare the ratios obtained to determine which shape and size yields the lowest possible volume-to-surface-area ratio.
To summarize, in order to have the lowest possible volume-to-surface-area ratio, we should choose a larger size and a shape that minimizes the surface area relative to the volume of the ice cube.