Unit 10: Surface Area and Volume
We frequently need to calculate the amount of space that exists inside an object. For example, we use the concept of volume to follow a recipe, but we also use it when we need to fill a moving box with books or packages, fill a moving van with boxes or furniture, fill a simple container with water, or fill a gas tank with gasoline.
Since containers come in so many shapes and sizes, in addition to simple square and rectangular boxes, learning how to calculate the amount of space that is available inside a three-dimensional object not only comes in handy, but can save you time, money, and create less waste.
Similarly, you may also need to calculate the amount of space that exists on the outside of an object, such as when you decide to paint your house or office. Making a few key calculations can ensure you buy the right amount of paint you need, the first time.
In this unit, we will investigate three dimensional shapes, and learn to calculate their surface areas and volumes.
Completing this unit should take you approximately 4 hours.
We first need to learn about three-dimensional figures, also known as polyhedrons.
Now, let's investigate the volume and surface area of different types of polyhedrons. The first type of polyhedron we study is the prism.
The next shape we study is the cylinder.
A pyramids is another type of three-dimensional polyhedron.
In this section we investigate cones.
The last simple shape we are going to investigate are spheres.
10.7: Composite Solids
Finally, we will use what we learned about regular polyhedrons to determine the volume and surface area of non-standard polyhedrons, or composite solids.