Question

Compare this level of uniformity to that of the surface of a square table that is 1 meter on each side: how big would the largest bumps on that table be if its surface were smooth to 1 part in 100,000?

Answer 1

The surface area to volume ratio can be used to determine the size of the largest bumps on a table if its surface were smooth to 1 part in 100,000. The exact calculation will depend on the dimensions and shape of the table.

Step-by-step explanation:

The question compares the level of uniformity of a surface to that of a square table. If the table's surface were smooth to 1 part in 100,000, the size of the largest bumps on the table can be determined. To calculate this, we can use the concept of surface area to volume ratio. We can compare the surface area of a shape to its volume to determine the ratio.

In this case, if we consider a single square meter of the table's surface and calculate the fraction of a cubic meter that melts, we can determine the size of the largest bumps. By ignoring the effect of air temperature, we can simplify the calculation.

The answer to the question will depend on the specific dimensions and shape of the table, as well as the uniformity required.

Answer 2

The largest bumps on a square table surface, if smooth to 1 part in 100,000, would be at most 0.01 mm in height, indicating an extremely smooth surface, comparable to the uniformity of the cosmic microwave background.

Step-by-step explanation:

The question asks to compare the uniformity of an idealized surface to that of the cosmic microwave background if a square table with a surface area of 1 square meter (m²) were smooth to 1 part in 100,000. To make this comparison, we could imagine a square table with a length of 1 meter (m) on each side. If the table were smooth to 1 part in 100,000, that would mean the largest imperfection or bump on this table could be no greater than 0.01 millimeters (mm), since 1 part in 100,000 of 1 meter is 0.01 mm (1,000,000 mm × (1/100,000)). This level of uniformity would be extraordinarily smooth and precise, similar to the uniformity of the cosmic microwave background's temperature variations.