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The Second Perfume Bottle (Mathematics)
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A perfume company is designing a second new perfume bottle.
The bottle is a cylinder.
The cylinder has height 5 cm and radius 2 cm.
The lid is a sphere with radius 1 cm.
Two bands of gold paint 6 mm wide go around the bottle.
The perfume company wants answers to these questions:
Part 1: Specifications
- They need to know the total area of gold that will be painted on each bottle in order to estimate the cost of this paint.
- The bottle is to hold 50 ml of perfume. Explain why this bottle is sufficiently big to hold this amount of liquid.
Part 2: Packaging
They are going to package the bottle i a cuboid box. The dimensions of the box will be the same width and depth as the base of the bottle and the total height of the bottle.
- They would like to know the volume inside the packaging that will be wasted because it will be empty.
- They need to know the amount of cardboard needed to make the box. Allow 50% more for construction.
Part 3: Designing a new bottle
They wanted to design a new bottle. The new bottle must be sufficiently big to hold 50 ml of perfume and have the same lid.
- Design a different perfume bottle and show that it meets the perfume company's specifications. Give a sketch of your new design, including the bands of gold paint, and clearly show the dimensions of your design. (You can use any different shape such as a cylinder, a prism, sphere or a pyramid, for the bottom part of the bottle).
- Compare the use of gold paint, amount of cardboard needed and wasted packaging space of your new design with the design of the original bottle, and comment on which design would be best, and why.
The bottle is a cylinder.
The cylinder has height 5 cm and radius 2 cm.
The lid is a sphere with radius 1 cm.
Two bands of gold paint 6 mm wide go around the bottle.
The perfume company wants answers to these questions:
Part 1: Specifications
- They need to know the total area of gold that will be painted on each bottle in order to estimate the cost of this paint.
- The bottle is to hold 50 ml of perfume. Explain why this bottle is sufficiently big to hold this amount of liquid.
Part 2: Packaging
They are going to package the bottle i a cuboid box. The dimensions of the box will be the same width and depth as the base of the bottle and the total height of the bottle.
- They would like to know the volume inside the packaging that will be wasted because it will be empty.
- They need to know the amount of cardboard needed to make the box. Allow 50% more for construction.
Part 3: Designing a new bottle
They wanted to design a new bottle. The new bottle must be sufficiently big to hold 50 ml of perfume and have the same lid.
- Design a different perfume bottle and show that it meets the perfume company's specifications. Give a sketch of your new design, including the bands of gold paint, and clearly show the dimensions of your design. (You can use any different shape such as a cylinder, a prism, sphere or a pyramid, for the bottom part of the bottle).
- Compare the use of gold paint, amount of cardboard needed and wasted packaging space of your new design with the design of the original bottle, and comment on which design would be best, and why.
Answers
Best Answer
No best answer has yet been selected by Horiana. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.It is actually quite straightforward although quite long, I have just enjoyed doing it when I should be working. You need the formulae for volume of a cylinder and a cuboid. Curved surface area of a cylinder and surface area of a box, add in a bit of logical thought and simple arithmetic. For your own designed bottle pick a shape that you understand the geometry of.
Totally pointless giving you the answers.
Totally pointless giving you the answers.
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