as i am new to calculus & probability,pls show how to do these problems(may be very trivial)

problem 1:show that the height of a right circular cylinder of the greatest volume that can be inscribed in a right circular cone is one-third of that of the cone.

(using derivatives and limits....)

problem 2:using integration,find the area enclosed by the curves $\displaystyle y= x^{2} $and$\displaystyle y=x+2 $

problem 3: out of 21 tickets marked with numbers from 1 to 21, three are drawn at random.Find the probability that the numbers on them are in A.P.

please help!!!thanks in advance