Category A Investigation # 11: Efficiency Ratios

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INVESTIGATION # 11

EFFICIENCY RATIOS

An efficiency ratio is the ratio of surface area to volume of a shape.

e.g.: A particular rectangular prism has a surface area of 88 cm² and a volume of 48 cm³. Its efficiency ratio is 88 ÷ 48 and is expressed as a percentage i.e. 183%. 

Efficiency ratios are important in biology with the study of heat loss of animals, and in physics with heat loss and gain of containers.

* Using the formulae given at the end of this page examine the efficiency ratios for various spheres, cubes, cones and cylinders.

* Look at which shape is the most efficient (i.e. has the LOWEST ratio).

* Look at how increasing the radius of a sphere or length of a cube affects its efficiency ratio.

* Look at how different shaped cones and cylinders have different efficiency ratios.

ASSESSMENT TASK

EFFICIENCY RATIOS

The formulae you require for this assessment are printed here:

1. Calculate the efficiency ratios for;

(a) A sphere of radius 3 cm ___________% (4 marks)

(b) A cube of edge length 7 cm __________% (4 marks)

(c) A cone with height and radius both 4 cm _________% (4 marks)

(d) A cylinder with height and radius both 5cm __________% (4 marks)

2. (a) If you are trying to find the most efficient shape for a vacuum flask to keep your coffee hot, which of the four shapes would you choose: sphere, cube, cone, cylinder; rank them in order from the least efficient to the most efficient. (Do NOT rely on the values in question 1).

______________,_______________,_______________,_______________ (4 marks)

 (b) The answer for question 2(a) can not be found from the results of question 1. Explain why not and how an answer could be found.

 _____________________________________________________________

 _____________________________________________________________.(2 marks)

3. As the radius of a sphere increases what happens to its efficiency ratio ?

___________________________________________________________. (2 marks)

4. The efficiency ratio for a cube is always .

Use the formulae to show why this is true. (3 marks)

5. A rodent with cylindrical body shape loses most of its heat from its body. Will a rodent with body length 10cm and radius approximately 5cm be more heat efficient than one with a length of 5cm and radius of approximately 10cm? Show working to justify your answer. (3 marks)

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