Volume of a Geometric Solid

Volume of a Geometric Solid5.10B-Connect Models for Volume with their Respective Formulas (Supporting Standard)

5.10C-Select & Use Appropriate Units and Formulas to Measure Volume (Readiness Standard)

Reasoning Mind Academy: Volume

Definition: is the number of cubic units (cm³ or in³) needed to fill a solid figure. Volume = How much can it hold?

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Volume Formula Cubic Units Length Width Height Edge Vertex Face


Definition: Volume is the number of cubic units (cm³ or in³) needed to fill a solid figure. Volume = How much can it hold?

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Definition: A is a rule that uses symbols. A formula can be used to calculate the volume of a shape or solid figure.

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Definition: A formula is a rule that uses symbols. A formula can be used to calculate the volume of a shape or solid figure.

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REMEMBER: Volume is measured in .

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REMEMBER: Volume is measured in cubic units .

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REMEMBER: In order to calculate the volume of a 3D figure, you must measure or know the

(how long it is!), (how wide it is!), and (how tall it is!) of the figure. These are called dimensions.

Key Words:Volume Formula Cubic Units Length Width Height Edge Vertex Face


REMEMBER: In order to calculate the volume of a 3D figure, you must measure or know the

length (how long it is!), width (how wide it is!), and height (how tall it is!) of the figure. These are called dimensions.

Key Words:Volume Formula Cubic Units Length Width Height Edge Vertex Face


Definition: A is one side of the 3D figure.

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Definition: A face is one side of the 3D figure.

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face

face

face


Definition: An is where two faces of a 3D figure meet or join each other.

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Definition: An edge is where two faces of a 3D figure meet or join each other.

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Definition: A is where two edges of a 3D figure meet or join each other.

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Definition: A vertex is where two edges of a 3D figure meet or join each other.

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List some similarities and differences of rectangular prisms and cubes! Rectangular Prism Cube


Label and count the number of faces, edges, and vertices!

10 cm

Faces: Faces: Edges: Edges: Vertices: _____ Vertices: _____


Label and count the number of faces, edges, and vertices!

10 cm

Faces: 6 Faces: 6Edges: 12 Edges: 12Vertices: 8_____ Vertices: 8____


Now, let’s have a scavenger hunt for the volume formulas used for certain solid figures!

3D Solid Figure

Cube

Rectangular Prism

Volume


Let’s try some volume EXAMPLES. Ex 1)

Find the volume of the rectangular prism above.


Let’s try some volume EXAMPLES. Ex 1)

Step 1: Draw a picture! (One is already drawn for you, but always use a picture.)

Step 2: Label your dimensions on the figure’s picture. (What units does the problem give you? They are already labeled for you! )


Step 3: Write your SFS = Shape, Formula, Substitute for the problem using the given dimensions.

Shape: Rectangular Prism

Formula: V= l x w x h

Substitute= V= 4 (cubic units) x 2 (cubic units) x 2 (cubic units)


Step 4: Multiply your dimensions.

V = (4 cubes) x (2 cubes) x (2 cubes) V = (8 cubes) x (2 cubes) V = 16


Step 5: Box your answer and write the correct units for your answer!

V = 16 cubic units

Example 2) A toy chest is shaped like a cube. It measures 2 feet, by 2 feet, by 2 feet. What is the volume of the toy chest?

Step 1: a picture! Step 2: your dimensions on the figure’s picture. (What units does the problem give you? )Step 3: your SFS = Shape, Formula, Substitute for the problem using the given dimensions. Shape: Formula: Substitute: Step 4: your dimensions.Step 5: Box your answer and write the correct for your answer!


Example 2) A toy chest is shaped like a cube. It measures 2 feet by 2 feet by 2 feet. What is the volume of the toy chest?

Step 1: Draw a picture! Step 2: Label your dimensions on the figure’s picture. (What units does the problem give you? )Step 3: Write your SFS = Shape, Formula, Substitute for the problem using the given dimensions. Shape: CubeFormula: V = s x s x sSubstitute: V = 2 (feet) x 2 (feet) x 2 (feet)Step 4: Multiply your dimensions.Step 5: Box your answer and write the correct units for your answer!


Example 3) Jim has a box that stores some gardening tools. The volume of the box is 160 cubic inches. The length of the box is 8 inches and the height is 5 inches. What is the width of the box?

*Hint: Use the steps you learned from example 1 and 2!


Example 3) Jim has a box that stores some gardening tools. The volume of the box is 160 cubic inches. The length of the box is 8 inches and the height is 5 inches. What is the width of the box? V= lxwxh160= 8x4x widthWidth = 5 inches

*Hint: Use the steps you learned from example 1 and 2!


Reasoning Mind Academy: “Now, it’s your turn to try!”

Independent Practice Problems

Helpful Hints:Read the problem twice.Underline any important parts.Make a plan for solving the problem.Show your work,Do your best!

Volume of a Geometric Solid

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