The idea here is that the difference between the mass of the empty container and the mass of the container + water will give you the mass of the water needed to fill the container.
At this point, you can use the density of water to figure out the volume of water, and consequently, the volume of the container.
So, you know that you have
#"mass of water" = overbrace("mass of container + water")^(color(blue)("gross mass")) - overbrace("mass of container")^(color(blue)("tare mass"))#
You can thus say that the water needed to fill the container has a mass of
#"mass of water" = "53.2165 g " - " 35.3343 g"#
#"mass of water = 17.8822 g"#
Now, you know that the density of water is equal to
Use the density of water as a conversion factor to calculate the volume of water needed to completely fill the container
#17.8822 color(red)(cancel(color(black)("g"))) * overbrace("1 mL"/(0.997color(red)(cancel(color(black)("g")))))^(color(blue)("the density of water")) = "17.9 mL"#
Since the volume of the container is equal to the volume of water it can hold, you can say that the volume of the container is equal to
#"volume container" = color(darkgreen)(ul(color(black)("17.9 mL")))#
The answer is rounded to three sig figs, the number of sig figs you have for the density of water at that temperature.