Answer:
See explanation below
Step-by-step explanation:
In order to explain this, is neccesary to draw both confomers, the cis and trans, but in the chair conformation, because in that way we can see much better the bonds and the reason of why the cis reacts faster than trans.
As you can see in picture attached, the more stable conformer is the one where the H and Br are in the axial position, and the tert butyl group in equatorial position. In these positions, the cis isomer can undergo an E2 reaction, and the ethoxide would have no problem to substract the hydrogen atom from the molecule to eliminate the Bromide. This is because the t-butyl group in equatorial position, is not exerting steric hindrance, therefore is faster.
In the case of the trans, the t-butyl group is in the axial position as well as the hydrogen and bromide, therefore, when the E2 reaction undergoes, the hydrogen is substracted by ethoxide, but it will be slow because the t.butyl group exerts steric hindrance in the axial positions, therefore, the hydrogen will be substracted slower than in the cis position. This is the main reason for the cis to be faster.
As for the second part of the question, which will be the answer of the whole question, see picture attached 2 for the whole sentence, and the match of the words is the following:
1. Axial
2. More
3. Blank (No word there)
4. less
5. Blank
6. Cis
7. Trans
8. Cis