Why are mathematical proofs important?

Really need on these. i have no idea what to do

In the surface area formula for cylinders which expressionrepresents the lateral area

Need ! the total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?