Why are the lower deck areas shaped like that, does that save some space? I find it common across lot of big aircraft.
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The answer lies in the existence of something called a Unit Load Device (ULD) -- basically a cargo pod for aircraft that's the equivalent of the shipping pallet.
ULDs allow oddly-shaped cargo (bags, assorted-size boxes, etc.) to be loaded efficiently in a standard volume and easily secured for flight (using hold-down lugs in the floor).
The shape of the cargo deck is designed to pack in as many ULDs as possible:

and as you can see from the cross-section the sloping sides on the bottom are a concession to the circular cross-section of the fuselage/pressure vessel.
Some other advantages of ULDs as they pertain to airline operations and baggage loading are described over on this question.
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Why not expand the cargo compartment to use the whole bottom half? – user253751 Aug 06 '15 at 23:57
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3There are a number of systems (e.g., power, flight controls, environmental ducts) routed through the spaces alongside & under the cargo area. – Ghillie Dhu Aug 07 '15 at 01:46
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1@immibis: Standardization. It's more economical to use a standard part for all aircraft than require each type of aircraft to use different containers. Conceivably, when ULDs were invented they use a higher % of the cross section of the average airliner. Nowdays widebodies are common so they end up using a smaller % of the cross-section. – slebetman Aug 07 '15 at 03:39
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@immibis I'm not sure what you mean by "the whole bottom half" -- are you saying just throw things into the bottom half-cylinder of the fuselage? If so, how will you accomplish the loading? (Hint: "Throw everything in there loose" doesn't work: It's inefficient in both space and time, and has other problems detailed in the post I linked to.) Similarly having half-cylinder ULDs doesn't work (they're too difficult to handle on the ground). ULDs trade a relatively small percentage of wasted space for enormous gains in cargo-handling efficiency. – voretaq7 Aug 07 '15 at 06:53
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@voretaq7 No. See the gap under the cargo bay in the photo, and the gaps to the sides - I meant expanding the cargo bay to use that space (and expanding the containers to fill the new cargo bay) – user253751 Aug 07 '15 at 06:55
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With airlines being cost-concious, I am sure they must be thinking of changing the design to accomodate more stuff... Good explanation none the less.. – Firee Aug 07 '15 at 09:31
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1@immibis: The bottom surface holds rails for quick loading. That's intentionally a horizontal surface. The space to the side is fairly small. – MSalters Aug 07 '15 at 09:35
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Does anybody have a similar cross section image for the A320. Couldn't find anything good in google. – Firee Jul 20 '16 at 10:27
