To find the number of revolutions the larger wheel with 14 cogs will make when the smaller wheel with 6 cogs makes 21 revolutions, you can use the concept of gear ratios. The ratio of the number of cogs on the smaller wheel to the number of cogs on the larger wheel is a key factor in determining their relative speeds and revolutions.

In this case, the ratio of cogs on the smaller wheel to cogs on the larger wheel is 6/14, which can be simplified to 3/7.

Now, if the smaller wheel makes 21 revolutions, the larger wheel will make:

Number of revolutions of larger wheel = (Number of revolutions of smaller wheel) * (Ratio of cogs on larger wheel to cogs on smaller wheel)

Number of revolutions of larger wheel = 21 * (3/7)

Number of revolutions of larger wheel = (21 * 3) / 7

Number of revolutions of larger wheel = 63 / 7

Number of revolutions of larger wheel = 9

So, the larger wheel with 14 cogs will make 9 revolutions when the smaller wheel with 6 cogs makes 21 revolutions.