Volume of Right Prisms

Unit 4, Lesson 13

Today’s standard: CCSS.MATH.CONTENT.7.G.B.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

How will you prove you understand this topic? By scoring at least 75% (3 out of 4) on the exit ticket.

With flat 2-D shapes, we filled up the shapes with unit squares and the number of squares was the area.

With 3-D shapes, we count up how many unit cubes it takes to fill the shape and that is the volume.

Volume = 8 cm³

Area = 5 units²

Page 1: Volume of a Prism

Remember, the volume will be the number of unit cubes that it takes to fill up the shape.

Is there a shortcut instead of counting the cubes one by one? Hint: Think about what we did when first learning about the area of rectangles.

Page 3: Math Mission

Explore and apply methods for finding the volume of a right prism.

Page 3: Work Time

The length multiplied by the width represents

_______________________________________

The height represents

_______________________________________

This picture shows that the formula for the volume of a rectangular prism is

_______________________________________

For any prism, if we know the area of the base, we would find the volume of the prism by

_______________________________________

Use the picture to help you complete each sentence.

Page 3: Work Time

The length multiplied by the width represents the number of cubes in one layer (area)

The height represents the number of layers.

Page 3: Work Time

Volume of rectangular prism = length x width x height

Volume of a prism = base x height

Page 4: Work Time

Only answer the first question:

If the area of the base of the regular pentagonalprism is 15 cm² and the height is 6 cm, what isthe volume of the prism?

Page 4: Work Time

Each of the 6 layers has an area of 15 cm² so the total volume is

Page 5: Work Time

Only solve the first problem (the triangular prism)

Notice that this is a scale drawing!

Direct Station We will continue in the next Pearson lesson to discover

the formula for volume of pyramids.

Independent Station You will begin planning for one part of the math

portion of the PBL.

You will be designing sets to use in your film. Of course, we don’t have the room to make full size sets so we will be shrinking everything down using scale factors.

This is like the design a bedroom activity – you will look up the real-life sizes of objects that you need in your video and then calculate the scale model size that you will use in your set.