5th Grade Math - Recognize Volume as Additive: CCSS.Math.Content.5.MD.C.5c

What is the volume of the figure below?

Screen shot 2015 12 22 at 11.21.49 am

Explanation

If you look closely at this figure, you can see that it is made up of two rectangular prisms. In order to solve for the volume, we need to find the volume of each rectangular prism and then add the volumes together to find the total.

Screen shot 2015 12 22 at 11.21.31 am

In order to find the length of the rectangular prism on the bottom, we had to take the height of the original figure (which was ) and subtract the height of the rectangular prism on the top (which is )

Now that we have the dimensions of both our rectangular prisms, we can solve for the volumes.

Remember, the formula for volume is

$v=l\times w\times h$

$v=10\times5\times3$ and $v=3\times5\times8$

and

Next, we add the volumes together to solve for the total volume of the original figure.

$\frac{\begin{array}[b]{r}150in^3\ +\ 120in^3\end{array}}{ \ \ \ \space 270in^3}$

*Remember, volume is always measured in cubic units!

John has a pool in his backyard that is $77\textup { cubic feet}$ . He wants to add a baby-pool that is $23\textup { cubic feet}$ . What will be the total volume of his pools?

Explanation

To solve this problem we simply need to remember that volume is additive. This means that we can add our two volumes together to find the combined, total volume.

$\frac{\begin{array}[b]{r}77ft^3\ +\ 23ft^3\end{array}}{ \ \space 100ft^3}$

Courtney has a pool in her backyard that is $60\textup { cubic feet}$ . She wants to add a baby-pool that is $20\textup { cubic feet}$ . What will be the total volume of her pools?

Explanation

To solve this problem we simply need to remember that volume is additive. This means that we can add our two volumes together to find the combined, total volume.

$\frac{\begin{array}[b]{r}60ft^3\ +\ 20ft^3\end{array}}{ \ \ \ \space 80ft^3}$

Lynn is going on a vacation. One of her suitcases has a volume of $12\textup { cubic feet}$ , and the other has a volume of $5\textup{ cubic feet}$ . What is the total volume of her two suitcases?

Explanation

To solve this problem we simply need to remember that volume is additive. This means that we can add our two volumes together to find the combined, total volume.

$\frac{\begin{array}[b]{r}12ft^3\ +\ 5ft^3\end{array}}{ \ \ \space 17ft^3}$

Linden has a pool in her backyard that is $58\textup { cubic feet}$ . She wants to add a baby-pool that is $15\textup { cubic feet}$ . What will be the total volume of her pools?

Explanation

To solve this problem we simply need to remember that volume is additive. This means that we can add our two volumes together to find the combined, total volume.

$\frac{\begin{array}[b]{r}58ft^3\ +\ 15ft^3\end{array}}{ \ \ \ \space 73ft^3}$

What is the volume of the figure below?

Screen shot 2015 12 22 at 11.25.38 am

Explanation

Screen shot 2015 12 22 at 11.25.56 am

Now that we have the dimensions of both our rectangular prisms, we can solve for the volumes.

Remember, the formula for volume is

$v=l\times w\times h$

$v=13\times4\times4$ and $v=4\times4\times11$

and

Next, we add the volumes together to solve for the total volume of the original figure.

$\frac{\begin{array}[b]{r}208in^3\ +\ 176in^3\end{array}}{ \ \ \ \space 384in^3}$

*Remember, volume is always measured in cubic units!

What is the volume of the figure below?

Screen shot 2015 12 22 at 9.45.56 am

Explanation

Screen shot 2015 12 22 at 9.46.17 am

In order to find the length of the rectangular prism on the right, we had to take the length of the original figure (which was ) and subtract the length of the rectangular prism on the left (which is )

Now that we have the dimensions of both our rectangular prisms, we can solve for the volumes.

Remember, the formula for volume is

$v=l\times w\times h$

$v=5\times3\times7$ and $v=4\times3\times4$

and

Next, we add the volumes together to solve for the total volume of the original figure.

$\frac{\begin{array}[b]{r}105in^3\ +\ 48in^3\end{array}}{ \ \ \space 153in^3}$

*Remember, volume is always measured in cubic units!

Brett is going on a vacation. One of his suitcases has a volume of $29\textup { cubic inches}$ , and the other has a volume of $20\textup{ cubic inches}$ . What is the total volume of his two suitcases?

Explanation

To solve this problem we simply need to remember that volume is additive. This means that we can add our two volumes together to find the combined, total volume.

$\frac{\begin{array}[b]{r}29in^3\ +\ 20in^3\end{array}}{ \ \ \ \space 49in^3}$

Marcus is adding an addition to his family room. Before the addition, his family room was $37\textup { cubic feet}$ . The addition is $22\textup { cubic feet}$ . After the addition, how big is the family room?

Explanation

To solve this problem we simply need to remember that volume is additive. This means that we can add our two volumes together to find the combined, total volume.

$\frac{\begin{array}[b]{r}37ft^3\ +\ 22ft^3\end{array}}{ \ \ \ \space 59ft^3}$