Define functional group, isomerism and explain if cyclopentane is an isomer of pentane. Draw structures for 4-ethyl-6-isopropyldecane and 6,6-diethyl-3,5,5-trimethylnonane.

The parent ring is a cyclohexane.

There are two ethyl groups and one methyl group.

Starting from the carbon with the methyl group and numbering clockwise gives 1-methyl, 3-ethyl, 5-ethyl. This simplifies to 1-methyl-3,5-diethyl.
Starting from one of the ethyl groups and numbering clockwise gives 1-ethyl, 3-methyl, 5-ethyl. This simplifies to 1,5-diethyl-3-methyl.
Starting from one of the ethyl groups and numbering counter-clockwise gives 1-ethyl, 3-ethyl, 5-methyl. This simplifies to 1,3-diethyl-5-methyl.
According to IUPAC rules, when there are different substituents, they are listed alphabetically. The numbering should give the lowest possible set of locants.
If we number to give the lowest set of locants, we get (1,3,5).
If we number such that the first substituent encountered gets the lowest number, and then proceed to give the next substituents the lowest numbers, and then prioritize alphabetical order for naming:
Option 1: 1-ethyl, 3-ethyl, 5-methyl $\rightarrow$ 1,3-diethyl-5-methylcyclohexane
Option 2: 1-methyl, 3-ethyl, 5-ethyl $\rightarrow$ 3,5-diethyl-1-methylcyclohexane
Both options give the locant set (1,3,5). When the locant sets are identical, alphabetical order of substituents determines the numbering. "Diethyl" comes before "methyl". So, the numbering should prioritize the ethyl groups.
Therefore, the correct numbering starts at one ethyl group as 1, the other ethyl group as 3, and the methyl group as 5.

The IUPAC name is $\boxed{\text{1,3-diethyl-5-methylcyclohexane}}$.