Napkin calc: assuming a driveway that's 20 feet wide and 30 feet long, the area will be 600 feet^2. The typical residential road's going to be something like 30 feet wide (enough for a parked car and two opposing lanes with comfort) and a guess at a block being like 1/20 of a mile, or 250 feet; that gives each city block of road about 7500 feet^2. So guessing conservatively, about one city block is probably at least 10 times larger than the driveway.
And that's before the actual road complexity. A city road also likely has to account for sewage, powerlines, telecom cables, drainage, etc. There's also a trade-off in road design: your friend likely never wants to build his driveway again, so he'll want something permanent like cement. But the city may want to make different trade-off; blacktop can be more easily maintained and expanded and upgraded than pavement, but also costs more in the long run (but pavement is more expensive up front).