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Cooling: efficient, single slot and most of all silent. It sized so big because it also has to cool down the additional HSI bridge chip that makes this card AGP compatible.
All the way at the back we find a big Molex connector. The card feeds from your Power Supply.
This my guru's is what we call a box. A container typically constructed with four sides perpendicular to the base and often having a lid or cover :)
Last but not least, the card live in action.