Final answer:
The British Settler Colony in South Africa lasted from 1806, when Britain took control of the Dutch Cape Colony, until 1910 when the Union of South Africa was formed.
Step-by-step explanation:
The duration of the British Settler Colony in South Africa began in 1806 when Britain took control over the Dutch Cape Colony. It continued through the period of increasingly aggressive British colonisation marked by events like the Great Trek and the discovery of valuable minerals. The Boer Wars were fought between the Boers and Britain for this territory, leading to the annexation of the South African Republic and the Orange Free State by the Cape Colony following the end of the second Boer War in 1902. Eventually, the British colonies and the former Boer republics came together to form the Union of South Africa in 1910. Thus, the answer to the duration of the British Settler Colony in South Africa is option 1) 1806-1910.