| Decompose figures to find volume | |
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| Description | |
| Exercise Name: | Decompose figures to find volume |
| Math Missions: | 5th grade (U.S.) Math Mission |
| Types of Problems: | 1 |
The Decompose figures to find volume exercise appears under the 5th grade (U.S.) Math Mission. This exercise develops an understanding of the addition postulate for volume by breaking a complicated shape into unit blocks.
Types of Problems[]
There is one type of problem in this exercise:
- Find the volume of the figure: This problem has a figure constructed out of unit blocks. The student is asked to find the volume by counting the blocks and then write the correct answer in the space provided.
Find the volume of the figure
Strategies[]
Knowledge of the volume formula is encouraged to ensure success on this exercise, but only an ability to count and visualize missing information is required.
- Blocks that are not visible can be assumed, so the figures do not break laws of gravity.
- To increase efficiency, sometimes the figure can be broken into several rectangular prisms, each of which can be found more quickly.
- The numerical answers do not go into triple digit numbers so they can be counted efficiently.
Real-life Applications[]
- Slicing a figure to find its volume motivates the volume formula that arises in Geometry.
- Breaking into blocks allows one to realize that volume has additive properties that are useful for applications such as building and cooking.
- The idea of volume is important for packing, shipping and cooking.
- Unit cubes can be used to efficiently store and package items. This is the main reason that boxes are generally rectangular prisms regardless of the items they carry.
- When one fills up their vehicle with gas, the volume of gasoline in their gas tank helps to determine their purchase. Whether they fill up with gallons or liters of gasoline or diesel, the amount is a volume calculation. On a smaller scale, when one fills up a gas can to take to another vehicle or to use the gas to power another device, they again use volume for measuring.
- The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.