The Goodsmell perfume company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to contain at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and the corresponding surface are and volume. This cylindrical perfume bottle needs to be boxed in a prism for sale on store shelves. The Goodsmell perfume company would like a box with the smallest possible surface area which will contain your design for the perfume bottle. Report the dimensions of the box and the corresponding area and volume.