Lesson 5

At this time, you may wish to include the volume scale factor and linear scale factor relationships in your Formula Sheet.

Example

A manufacturer of gasoline barrels was determining what effect changing dimensions would have on the capacity of the company’s cylindrical barrels. The company started with a barrel that had a capacity of 1 L.

1. What will the barrel’s capacity be if only the barrel’s height is doubled?
   
   
2. What will the barrel’s capacity be if only the barrel’s radius is doubled?
   
   
3. Calculate the barrel’s capacity if both the barrel’s height and radius are doubled.

Solution

1. If just the height is doubled, it is logical to see that the capacity is doubled. It is like putting another 1-L barrel on top of the original 1-L barrel. The manufacturer will have 2 L.

    

   
   
   

2. If the radius is doubled, it is like doubling both the length and width. So, the capacity will be 2 x 2, or 4, times as great. The barrel will have a capacity of 4 L.
   
   This is easy to see if you look at the formula for the volume of a cylinder.

    

    
   

    

   
   
   

3. Remember what you learned in parts a. and b. If both the radius and height are doubled, you will have factors of 2 (for the height change) and 4 (for the radius change). The capacity will be
   
   

   
   
   
   

Self-Check 1

1.  
   1. How will the capacity of a swimming pool change if the pool’s length and width are tripled? Answer

    

   2. How will the capacity of a swimming pool change if the pool’s depth, length, and width are all tripled? Answer

    

   3. How will the capacity of a swimming pool change if the pool’s depth remains the same, but the length is doubled and the width is tripled? Answer
      
      
2. Comstock/Thinkstock
   Jeremy is shopping for oranges. He notices that not all oranges are the same size. One orange is 1.5 times the diameter of another. How many times greater is the volume of the large orange? Answer
   
   
3. iStockphoto/Thinkstock
   A model train locomotive is built to 1:32 scale. How many times larger in volume is the actual locomotive? Answer
   
   
4. The planets in the solar system are all approximately spheres. If Uranus has a volume 64 times that of Earth, what is the relationship between the two planets’ radii? Answer