The liquid column of a liquid-in-glass thermometer (4 cm at 10 °C, 16 cm at 100 °C) has a length of 10 cm at

It seems like you're asking for the temperature corresponding to a 10 cm liquid column in a liquid-in-glass thermometer. To find this, we can use the concept of linear interpolation.

Here are the steps:

1. First, we need to understand the scale of the thermometer. We know that at 10°C the liquid column is 4 cm and at 100°C it's 16 cm. So, the range of temperature (100°C - 10°C = 90°C) corresponds to a range of 12 cm in the liquid column (16 cm - 4 cm = 12 cm).

2. This means that each 1°C change in temperature corresponds to a change of 12 cm / 90°C = 0.133 cm/°C in the liquid column.

3. Now, we want to find the temperature corresponding to a 10 cm liquid column. First, we find the difference in length from the 10°C reference point: 10 cm - 4 cm = 6 cm.

4. Finally, we divide this length difference by the cm/°C ratio to find the corresponding temperature difference: 6 cm / 0.133 cm/°C = 45°C.

5. We add this temperature difference to the reference temperature of 10°C: 10°C + 45°C = 55°C.

So, a 10 cm liquid column corresponds to a temperature of 55°C.