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Volume of a Geometric Solid

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Volume of a Geometric Solid

5.10B-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?

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

Definition: Volumeis the number of cubic units (cm³ or in³) needed to fill a solid figure.

Volume = How much can it hold?

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

Key Words:

VolumeFormula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

REMEMBER: Volume is measured in .

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

REMEMBER: Volume is measured in cubicunits.

Key Words:

Volume FormulaCubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

face

face

face

Reasoning Mind Academy: Volume

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

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertex Face

Reasoning Mind Academy: Volume

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

Key Words:

Volume Formula Cubic Units

LengthWidth Height

EdgeVertexFace

Reasoning Mind Academy: Volume

List some similarities and differences of rectangular prisms and cubes!

Rectangular

PrismCube

Reasoning Mind Academy: Volume

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

10cm

Faces: Faces:

Edges: Edges:

Vertices: _____Vertices: _____

Reasoning Mind Academy: Volume

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

10cm

Faces: 6Faces: 6

Edges: 12Edges: 12

Vertices: 8_____ Vertices: 8____

Reasoning Mind Academy: Volume

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

Reasoning Mind Academy: Volume

Let’s try some volume EXAMPLES.

Ex 1)

Find the volume of the rectangular prism above.

Reasoning Mind Academy: Volume

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! )

Reasoning Mind Academy: Volume

Step 3: Writeyour 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)

Reasoning Mind Academy: Volume

Step 4: Multiply your dimensions.

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

V = (8 cubes) x (2 cubes)

V = 16

Reasoning Mind Academy: Volume

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

V = 16 cubic units

Reasoning Mind Academy: Volume

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!

Reasoning Mind Academy: Volume

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: Writeyour SFS = Shape, Formula, Substitute for the problem using the given dimensions.

Shape:Cube

Formula: V = s x s x s

Substitute: 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!

Reasoning Mind Academy: Volume

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!

Reasoning Mind Academy: Volume

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= lxwxh

160= 8x4x width

Width = 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!