Do you remember the activity about the boxes that contain cans inside of them? All cans are usually packaged in a rectangular prisms where it is sombody's job to calculate the surface area and the volume of the boxes to see if all the cans will fit in it. In this investigation we will learn how to calculate the surface area and volume with the appropiate units of a rectangular prism. Also, we will know how to express the final area in the correct units, like the square units or cubic units. As well, we will learn all the steps of the surface area and volume of a rectangular prism in which we will apply the knowledge learned in real life situations.
Key Vocabulary:
1. Volume: Is the number of unit cubes that it would take to fill a box. It also is the amount of space occuppied by, or the capacity of a 3 - dimencional shape.
2. Surface Area: Is the total area of all of its faces. Also the area required to cover a 3 - dimencional shape.
3. Prism: A 3 - dimensional shape with a top and bottom that are congruent polygons and lateral faces that are parallelograms.
4. Base: The face of 3 - dimensional shape chosen to be the bottom face.
5. Rectangular Prism: A prism with a top and bottom that are congruent rectangules.Task Analysis:
SURFACE AREA:
1. Find all the areas of the 3 distinct faces.2. Add all the answers of the 3 - dimensional areas.
3. Multiply the answer by 2.
4. Put the corresponding units2.
5. Equation: 2 x ( L x W + W x H + H x L ) = Surface Area.
VOLUME:
1. Multiply the 3 distinct sides lengths.
2. Put the corresponding units3.3. Equation: L x W x H = Volume.
Example:
1. Using the diagram below you will answer the following questions.
1A. Draw the prisms with the corresponding measurements.
1B. Find the volume of the rectangular prism with the correct units.
- 5 x 4 x 10 = 200 cm3
1C. Find the surface area of the rectangular prism with correct units.
- 2 x ( 5 x 4 + 4 x 10 + 10 x 5) = 2,500cm2.
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