# Volume of Right Prisms

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Examples, videos, and solutions to help Grade 7 students learn how to use the formula V = bh to determine the volume of a right prism.

### New York State Common Core Math Grade 7, Module 6, Lesson 25

Worksheets for 7th Grade, Module 6, Lesson 25 (pdf)

### Lessons 25 Student Outcomes

• Students use the formula to determine the volume of a right prism. Students identify the base and compute the area of the base by decomposing it into pieces.

### Lessons 25 Summary

• The formula for the volume of a prism is V = bh, where is the area of the base of the prism. A base that is neither a rectangle nor a triangle must be decomposed into rectangles and triangles in order to find the area of the base.

Lesson 25 Classwork

Opening Exercise
Take your copy of the following figure, and cut it into four pieces along the dotted lines (the vertical line is the altitude, and the horizontal line joins the midpoints of the two sides of the triangle).
Arrange the four pieces so that they fit together to form a rectangle.
If a prism were formed out of each shape, the original triangle and your newly rearranged rectangle, and both prisms had the same height, would they have the same volume? Discuss with a partner.

Exercise 1
a. Show that the following figures have equal volumes.
b. How can it be shown that the prisms will have equal volumes without completing the entire calculation?

Example 1
Calculate the volume of the following prism.

Example 2
A container is shaped like a right pentagonal prism with an open top. When a cubic foot of water is dumped into the container, the depth of the water is inches. Find the area of the pentagonal base.

Example 3
Two containers are shaped like right triangular prisms each with the same height. The base area of the larger container is 200% more than the base area of the smaller container. How many times must the smaller container be filled with water and poured into the larger container in order to fill the larger container?

Exercise 3
Two aquariums are shaped like right rectangular prisms. The ratio of the dimensions of the larger aquarium to the dimensions of the smaller aquarium is 3:2.
Addie says the larger aquarium holds 50% more water than the smaller aquarium.
Berry says that the larger aquarium holds 150% more water.
Cathy says that the larger aquarium holds over 200% more water.
Are any of the girls correct? Explain your reasoning.

Example 1

Find the volume of the following three-dimensional object composed of two right rectangular prisms.

Example 2

Calculate the volume of the following prism.

Example 3

A container is shaped like a right pentagonal prism with an open top. When a cubic foot of water is dumped into the container, the depth of the water is inches. Find the area of the pentagonal base.

Example 4
Find the volume of the right prism shown in the diagram whose base is the region between two right triangles.

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