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.

The Pretty Perfume company, Goodsmell's competition, has also designed a new perfume bottle. The bottle is to be a spherical shape with a diameter of 7cm. Determine the volume and surface area of this bottle.

The spherical bottle has a conical shaped lid with a diameter of 5cm and a height of 4.5cm. Given this information, calculate the volume and surface area of the lid of the spherical shaped bottle.

Determine the dimensions of the smallest possible box which could be used to package Pretty Perfume's new bottle with its spherical bottle and conical-shaped lid. However, this box is not shaped like a rectangular prism. Pretty Perfume would like to have unique packaging and have chosen to have a box shaped like a pyramid. Calculate the volume and surface area of this pyramid-shaped box.

The Final Product:

Prepare a written report that includes:

A clear and concise explanation of the process that you used to solve the problem.
The calculations that you made, presented in an organized fashion.
A rationale (reason) for your selection of values.
A conclusion which states each of your findings rounded to one decimal place.