A typical o-furo has about the same volume as a western bath, but is shorter and deeper. A water heater is attached directly to the o-furo, so you fill it and then turn on the heater for twenty minutes or so (and if you accidentally drain the water with the heater still on, you'll end up with a melted water heater). The o-furo in sento (communal bath house) and onsen (hot springs) are much bigger. The rules, though, remain the same: you wash outside the o-furo before getting in. Thus, the typical Japanese bathroom (literally a "bath room") has a tiled floor and drains.
Terms of address
A useful compendium of Mormon ecclesiastical and theological terminology can be found here.