An open box is to be constructed from a piece of cardboard 8 inches by 8 inches by cutting squares from each corner and then folding up the sides. Given that the removed squares have a side length of inches, express the volume of the box in terms of as a polynomial in standard form.
A right circular cone has a radius of and its height is 3 units less than its radius. Express the volume of the cone as a polynomial function, knowing that the volume of a cone with radius and height is .
A cylinder has a radius of units and its height is 3 units greater than its radius. Express the volume of the cylinder in the form , where is a polynomial in standard form.
A rectangle has a length of 10 units and a width of 8 units. Squares of by units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of .