Modeling Objects with Geometric Shapes

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When it comes to using geometry to solve real-world problems, in this lesson, you'll learn how modeling your real-world problem with a common geometric shape can help you to easily solve the problem.

Geometric Shapes

In this lesson, we'll take a look at you can use geometric shapes to help you solve real-world problems. Remember, your geometric shapes are shapes that have a distinct exterior and an interior. Many geometric shapes also have distinct corners and edges. For example, your triangle has three corners and three sides. Your circle, on the other hand, has a round exterior surrounding its interior. Each geometric shape comes with its own set of equations for finding the perimeter, area, and volume. It is these equations that make these shapes so very useful.

A Triangle and a Circle
geometric modeling

Modeling Real-World Objects

In fact, you can use these geometric shapes and their respective equations to help you solve real-world problems. The way you use geometric shapes to help you solve real-world problems is by modeling your real-world problem with a matching geometric shape. For example, if you were trying to figure out how much carpet you need to completely carpet a rectangular living room, you can model the living room with a rectangle. You can then use all the equations related to that rectangle to help you solve your problem. To figure out how much carpet you need, you can use the area formula for a rectangle. This will tell you just how much space you have in your rectangle, your living room.

A Rectangular Living Room
geometric modeling

Let's take a look at a couple of examples to see how this works.

Example 1

Sally likes to build her own things. She has just finished building her very own fish tank. It measures 2 feet wide by 2 feet long by 2 feet high. How many gallons of water can her fish tank hold?

You can solve this problem by modeling Sally's fish tank with a cube. If you look at her dimensions, they give you a cube that is 2 feet long on all sides. Now that you've modeled your problem with a geometric shape, you can now use its respective equations to help you solve your problems. In this case, you need the equation for volume to find out how much space is inside the cube. You remember that the equation for the volume of a cube is the length of a side cubed. So, you take your 2, and you cube it.

A Cube Fish Tank
geometric modeling

V = 2^3 = 8.

You get an answer of 8 cubic feet. Now, to convert this to gallons, you need the conversion factor. You look this up either online or in your math reference book. You find the conversion factor to be 1 cubic foot is equal to 7.48 US gallons. So, to convert your 8 cubic feet to gallons, you multiply your 8 by 7.48. You get this:

8 * 7.48 = 59.84 gallons.

Now Sally knows how much water her fish tank will hold. This will help her as she takes care of her tank and adds necessary cleaners and nutrients into the water.

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