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The Volume of a Right Prism




 

Video solutions to help Grade 7 students learn how to use the formula to find the volume of a right rectangular prism.


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Common Core For Grade 7

New York State Common Core Math Grade 7, Module 3, Lesson 23


Lesson 23 Student Outcomes


• Students use the known formula for the volume of a right rectangular prism (length x width x height).
• Students understand the volume of a right prism to be the area of the base times the height.
• Students compute volumes of right prisms involving fractional values for length.

Lesson 23 Classwork

Opening Exercise
The volume of a solid is a quantity given by the number of unit cubes needed to fill the solid. Most solids - rocks, baseballs, people - cannot be filled with unit cubes or assembled from cubes. Yet such solids still have volume. Fortunately, we do not need to assemble solids from unit cubes in order to calculate their volume. One of the first interesting examples of a solid that cannot be assembled from cubes but whose volume can still be calculated from a formula is a right triangular prism.
What is the area of the square pictured on the right? Explain.
Draw the diagonal joining the two given points then darken the grid lines within the lower triangular region. What is area of that triangular region? Explain.

Example 1: The Volume of a Right Prism
What is the volume of the right prism pictured on the right? Explain.
Draw the same diagonal on the square base as done above then darken the grid lines on the lower right triangular prism. What is the volume of that right triangular prism? Explain.
How could we create a right triangular prism with five times the volume of the right triangular prism pictured to the right, without changing the base? Draw your solution on the diagram, give the volume of the solid, and explain why your solution has five times the volume of the triangular prism.

What could we do to cut the volume of the right triangular prism pictured on the right in half without changing the base? Draw your solution on the diagram, give the volume of the solid, and explain why your solution has half the volume of the given triangular prism.

Example 2: The Volume of a Right Triangular Prism
Find the volume of the right triangular prism shown in the diagram using V = Bh.

Exercise 1: Multiple Volume Representations
The right pentagonal prism is composed of a right rectangular prism joined with a right triangular prism. Find the volume of the right pentagonal prism shown in the diagram using two different strategies.




Closing
• What are some strategies that we can use to find the volume of three-dimensional objects?
• Find the area of the base, then multiply times the prism’s height; decompose the prism into two or more smaller prisms of the same height and add the volumes of those smaller prisms.
• The volume of a solid is always greater than or equal to zero.
• If two solids are identical, they have equal volumes.
• If a solid S is the union of two non-overlapping solids A and B, then the volume of solid S is equal to the sum of the volumes of solids A and B.


 

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