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### Volume

Finding Combined Volume Using Formulas

How can we find Volume?

How can we find volume?

- Multiplication
- Counting cubic units.
- Using Formulas
- V= l x w x h
- V = Base x h

Volume Formulas

- V = l x w x h l = length w = width h = height
- V = B x h B= Base (area)
h = height

height

width

length

Base

height

Modeled Practice: Figure Included

Find the volume of the figure below:

Step 1 – Write down the formula for each figure . V= l x w x h

Step 2 - Identify the length (10), width(4) and height(5) for the bottom figure. Identify the length (5), width(2) and height (3) for the top figure.

Step 3 – Insert the values for length, width and height into the formulas. V = 10 x 4 x 5 V = 5 x 2 x 3

Step 4 – Multiply and solve for volume of each figure. V = 200 cubic units V = 30 cubic units

Step 5 – Add the volumes together to find the combined volume. V = 200 + 30, V = 230 cubic units

5

3

2

5

10

4

Modeled Practice: Figure not Included

Find the volume of a figure with the following dimensions:Figure (top) :length = 4cm height = 6 cm width = 2 cm

Figure (bottom) : length = 6 cm height = 2 cm width = 1cm

Step 1 – Write down the formula for each figure . V= l x w x h

Step 2 - Identify the length (6cm), width(1cm) and height(2cm) for the bottom figure. Identify the length (4cm), width(2cm) and height (6cm) for the top figure.

Step 3 – Insert the values for length, width and height into the formulas. V = 6 x 1 x 2 V = 4 x 2 x 6

Step 4 – Multiply and solve for volume of each figure. V = 12 cm³ V = 48 cm³

Step 5 – Add the volumes together to find the combined volume. V = 12 + 48, V = 60 cm³

Guided Practice: Figure Included

Find the volume of the figure below:

Step 1 – Write down the formula for each figure . V= l x w x h

Step 2 - Identify the length, width, and height for the bottom figure. Identify the length, width and height for the top figure.

Step 3 – Insert the values for length, width and height into the formulas.

Step 4 – Multiply and solve for volume of each figure.

Step 5 – Add the volumes together to find the combined volume.

4

1

2

3

8

2

Guided Practice: Figure not Included

Find the volume of a figure with the following dimensions:Figure (top) :length = 2 cm height = 4 cm width = 9 cm

Figure (bottom) : length = 7 cm height = 2 cm width = 8cm

Step 1 – Write down the formula for each figure . V= l x w x h

Step 2 - Identify the length, width and height for the bottom figure. Identify the length, width, and height for the top figure.

Step 3 – Insert the values for length, width and height into the formulas.

Step 4 – Multiply and solve for volume of each figure.

Step 5 – Add the volumes together to find the combined volume.

WORD PROBLEM

Lisandra is baking a two layer cake. The top cake has a height of 3 inches, a length that is 6 inches and a width that is 3 inches. The bottom cake has a height of 2 inches, a length of 3 inches and a width of 3 inches. What is the volume of Lisandra’s cake?

Word Problems Guided

Step 1 – Draw the model

Step 2 - Write down the formula for each figure . V= l x w x h

Step 3 - Identify the length, width and height for the bottom figure. Identify the length, width, and height for the top figure.

Step 4 – Insert the values for length, width and height into the formulas.

Step 5 – Multiply and solve for volume of each figure.

Step 6 – Add the volumes together to find the combined volume.

GUIDED WORD PROBLEM

Kai has an pile of books on his desk. The bottom book has a height of 12 inches, a length that is 6 inches and a width that is 5 inches. The top book has a height of 3 inches, a width of five inches and a length of two inches. What is the combined volume of Kai’s books?

Word Problems Guided

Step 1 – Draw the model

Step 2 - Write down the formula for each figure . V= l x w x h

Step 3 - Identify the length, width and height for the bottom figure. Identify the length, width, and height for the top figure.

Step 4 – Insert the values for length, width and height into the formulas.

Step 5 – Multiply and solve for volume of each figure.

Step 6 – Add the volumes together to find the combined volume.

Independent Practice

With a small group find the combined volume of the stacked books at your table. Use the ruler to measure the length of the books in inches. Write a short paragraph describing the steps you took in solving the problem.

REVIEW

What did we learn today?

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