Final answer:
The water should be added until it reaches 10.5 cm in height, which is half the full height of the 21 cm tall beaker, taking option (a) as the correct answer.
Step-by-step explanation:
To find the height to which water must be filled in the beaker so that it looks half of its filled capacity, we can rely on simple arithmetic. Given that the beaker has a height of 21 cm, to appear half full, we would naturally think to fill it to 10.5 cm. However, this would not take into account the properties of water and the container, or any other physical or optical effects.
In the absence of any additional information about the shape of the beaker or how 'looking half full' might differ from actually being half full due to optical effects or container shape (which can't be ignored in certain physics problems, like those involving water and capillarity or containers with varying diameters), the straightforward answer to the problem is half of the total height of the beaker.
Therefore, the water should be added until it reaches 10.5 cm in height, which is option (a). This is the correct answer under normal conditions and with the assumption that the beaker's interior is uniform and there are no optical effects in question.