In order to use the wifi here, i had to connect to the network and then be accepted by the director's computer. does this make them able to see what i browse online?

Yes
it does any internet you use the owner of the router can see it some hackers set up hotspots to steal information from your phone

Hypothesis: volumes of both figures are equal.the volume of  figure 1 is: .the volume of figure 2 is: .since , you can conclude that and . so, .volumes of figures are equal only when an angle in the basis is right (then figures will be the same), in another cases volume of figure 1 is less than volume of figure 2.the hypothesis was not correct in all cases.