1. A storage system, comprising: a first virtual volume that is constituted by a plurality of virtual areas and is based on thin provisioning technology; a second virtual volume that is based on storage virtualization technology and corresponds with an external logical volume that is formed based on a removable external storage device; a pool that has a plurality of pages which are storage areas that can be assigned to the virtual areas of the first virtual volume; mapping information that indicates which of the plurality of pages correspond with which virtual areas; an I/O processing unit that receives a write request from a computer, assigns a page in the pool to a virtual area of the first virtual volume that is designated by the write request, writes data fragments corresponding to the write request to the assigned page, and associates information representing the page with information representing the virtual area to which the page is assigned, in the mapping information; a backup processing unit that copies a plurality of data fragments that are stored in each of a plurality of pages that are assigned to the first virtual volume to the second virtual volume, the plurality of data fragments being serially arranged in the second virtual volume, updates information representing the respective copy source pages in the mapping information to information that represents respective copy destination pages for the data fragments stored in the respective copy source pages, and copies the updated mapping information to the second virtual volume; and a restore processing unit that reads the mapping information from the second virtual volume and provides the computer with a restore virtual volume which is a virtual volume based on the mapping information without executing restore copy processing that reads a plurality of data fragments specified by the mapping information from the second virtual volume and copies the plurality of data fragments to a plurality of pages which are assigned to a plurality of virtual areas, in the restore virtual volume, specified by the mapping information, wherein the I/O processing unit receives a read request, from the computer, that designates the restore virtual volume, specifies the storage area which is in the second virtual volume and corresponds with the virtual area designated by the read request from the mapping information, reads data fragment from the specified storage area, and transmits the data fragment to the computer, and wherein the I/O processing unit does not accept a write request, from the computer that designates the restore virtual volume.