Suppose that $x, y,z$ are positive integers satisfying $x <= y <= z$, and such that the product of all three numbers is twice their sum. What is the sum of all possible values of $z$?

Find the volume of the solid generated when the region bounded by y= x and y= 4√x is revolved about the x-axis the volume of the solid is: (type an exact answer cubic units)

The perimeter of a rectangle is greater than or equal to 74 meters. if the length is 25 meters, the minimum width of the rectangle is meters.

The figures below are made out of circles, semicircles, quarter circles, and a square. find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).