Please Check my work and help me to answer the questions i could not get.

Measure the cube that you are given. Complete the chart on the next page for your cube, then fill in the spaces for two other cubes, one measuring 1 cm on an edge and the other measuring 0.5 cm on a side. The ratio of surface area volume should be divided so that it is expressed as square cm per cubic cm.

Your Cube:
(1)Length of 1 Edge- 2.5
(2)Area of One Side- 6.25
(3)Total Surface Area- 37.5
(4)Volume- 2.5 squared
(5)Ratio of SA/Volume (reduced to /1 cc)-

1 cm cube:
(1) 1
(2) 1
(3) 6
(4)1 squared
(5)?

.5 CM cube:
(1) .5
(2) .25
(3) 18
(4) .5 squared
(5) ?

Please check the above math and help. Also:

1. If a cell is made smaller and smaller, what happens to the ratio of surface area to volume. (It Decreases?)
2. Of what value is it to a cell to have a large surface area to volume ratio?
3. How does having small cells affect the metabolic rate that is possible in these cells?

Thanks

Let's check your work:

Your Cube:
(1) Length of 1 Edge: 2.5 cm (Looks correct)
(2) Area of One Side: 2.5 cm x 2.5 cm = 6.25 cm^2 (Correct)
(3) Total Surface Area: 6 sides x 6.25 cm^2 = 37.5 cm^2 (Correct)
(4) Volume: 2.5 cm x 2.5 cm x 2.5 cm = 15.625 cm^3 (Incorrect, you need to cube the length, so it should be 2.5^3 = 15.625)
(5) Ratio of SA/Volume (reduced to /1 cc): 37.5 cm^2 / 15.625 cm^3 = 2.4 cm^-1 (Correct)

1 cm cube:
(1) Length of 1 Edge: 1 cm (Correct)
(2) Area of One Side: 1 cm x 1 cm = 1 cm^2 (Correct)
(3) Total Surface Area: 6 sides x 1 cm^2 = 6 cm^2 (Correct)
(4) Volume: 1 cm x 1 cm x 1 cm = 1 cm^3 (Correct)
(5) Ratio of SA/Volume: 6 cm^2 / 1 cm^3 = 6 cm^-1 (Correct)

0.5 cm cube:
(1) Length of 1 Edge: 0.5 cm (Correct)
(2) Area of One Side: 0.5 cm x 0.5 cm = 0.25 cm^2 (Correct)
(3) Total Surface Area: 6 sides x 0.25 cm^2 = 1.5 cm^2 (Correct)
(4) Volume: 0.5 cm x 0.5 cm x 0.5 cm = 0.125 cm^3 (Correct)
(5) Ratio of SA/Volume: 1.5 cm^2 / 0.125 cm^3 = 12 cm^-1 (Correct)

Now let's answer your other questions:

1. If a cell is made smaller and smaller, what happens to the ratio of surface area to volume?
As the cell becomes smaller, the ratio of surface area to volume increases. This is because the surface area decreases more rapidly than the volume. The surface area is proportional to the square of the length, while the volume is proportional to the cube of the length.

2. Of what value is it to a cell to have a large surface area to volume ratio?
A large surface area to volume ratio is beneficial for a cell because it allows for efficient exchange of nutrients, gases, and waste products with its environment. A high surface area enables a cell to take in more resources and eliminate waste more quickly, which is crucial for cellular functions.

3. How does having small cells affect the metabolic rate that is possible in these cells?
Having small cells can lead to a higher metabolic rate. Since small cells have a larger surface area relative to their volume, they have a greater capacity for nutrient uptake and waste elimination. This enhances their metabolic efficiency and enables them to carry out chemical reactions at a faster rate.