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If you are not leaving the airport transit area and the bags are checked through, you don't need a transit visa, no matter which country you are from.
To take the city tour, you have to actually enter the country. For that, you should have a visa, or from a country that doesn't need a visa, or is eligible for Visa Free Transit Facility. Since you do not qualify for any of that, you should take a visa to take the city tour.
My advice is to stay at the Airport. It's not like your usual airport. There are many things you can do in 10 hours at the airport, including numerous gardens, swimming pools, movie theatres, etc. You might be eligible for lounge access also. Check the website for more details.
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If you stay inside the terminal, you do not need a visa:
Travellers at Singapore Changi Airport who are in transit and who are not seeking entry into Singapore, do not need to apply for a visa if they remain in the transit area and do not cross immigration. Travellers are advised to inquire with the respective airlines in their itinerary if they are required to cross immigration in order to change terminals or to formally check-in again before continuing with the subsequent leg of their journey.
If you bought your flight as a single through ticket, then this will likely be the case. However, if you have booked your flights as separate tickets, and are traveling with hold luggage or you are required to check in in the departures hall then you would need to enter Singapore, and would therefore need a visa.
Singapore airlines does offer a free tour for long layovers, but you must enter Singapore to go on the tour, and you would therefore need a visa.