 # Volume of Non-overlapping Rectangular Prisms

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Common Core For Grade 5

Videos, examples, and solutions to help Grade 5 students learn how to find the total volume of solid figures composed of two non-overlapping rectangular prisms.

New York State Common Core Math Grade 5, Module 5, Lesson 6
Common Core Standards: 5.MD.3, 5.MD.5
Common Core Math Grade 5, Module 5, Lesson 6 Worksheets (pdf)

Lesson 6 Concept Development

Problem 1
Build and combine structures then find the total volume.

Problem 2
What is the volume of this prism with dimensions 3m x 2m x 7m?

Problem 3
How is this drawing different from the last one?

Problem 4
Compare this figure to the last one.

Problem 5
Two rectangular prisms have a combined volume of 135 cubic meters. Prism A has double the volume of Prism B.
a. What is the volume of each prism?
b. If one face of Prism A has an area of 10 square meters, what is its height? Lesson 6 Problem Set

1. Find the total volume of the figures and record your solution strategy. Volume: _____________
Solution Strategy:

2. A sculpture (pictured below) is made of two sizes of rectangular prisms. One size measures 13 in by 8 in by 2 in. The other size measures 9 in by 8 in by 18 in. What is the total volume of the sculpture?

3. The combined volume of two identical cubes is 128 cubic centimeters. What is the side length of each cube?

5. Two rectangular prisms have a combined volume of 432 cubic feet. Prism A has half the volume of Prism B.
a. What is the volume of Prism A? Prism B?
b. If Prism A has a base area of 24 ft2, what is the height of Prism A?
c. If Prism B's base is 2/3 the area of Prism A's base, what is the height of Prism B?

Lesson 6 Homework

This video shows how to find the volume of multiple solids by first calculating for missing dimensions.

1. Find the total volume of the figures and record your solution strategy.

2. A planting box (pictured below) is made of two sizes of rectangular prisms. One type of prism measures 3 inches by 6 inches by 14 inches. The other type measures 18 inches by 9 inches by 10 inches. What is total volume of three such boxes? 1. Find the total volume of the figures and record your solution strategy. Lesson 6 Homework

3. The combined volume of two identical cubes is cubic centimeters. What is the measure of one cube’s edge?
Lesson 6 Homework

4. A fish tank has a base area of 45 cm2 and is filled with water to a depth of 12 cm. If the height of the tank is 25 cm, how much more water will be needed to fill the tank to the brim?

5. Three rectangular prisms have a combined volume of 518 cubic feet. Prism A has one-third the volume of Prism B, and Prisms B and C have equal volume. What is the volume of each prism?

Lesson 6 Homework

1. Find the total volume of the figures and record your solution strategy.

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