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

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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Example Questions

Example Question #1 : Recognize Volume As Additive: Ccss.Math.Content.5.Md.C.5c

Erica is going on a vacation. One of her suitcases has a volume of 3 cubic feet, and the other has a volume of 2 cubic feet. What is the total volume of Erica's two suitcases?

Possible Answers:

5 cubic feet

Not enough information

1 cubic foot

25 cubic feet

6 cubic feet

Correct answer:

5 cubic feet

Explanation:

 

 

 

Example Question #1801 : Common Core Math: Grade 5

What is the volume of the figure below? 

Screen shot 2015 12 22 at 9.34.52 am

Possible Answers:

\(\displaystyle 48in^2\)

\(\displaystyle 132in^3\)

\(\displaystyle 132in^2\)

\(\displaystyle 84in^3\)

\(\displaystyle 48in^3\)

Correct answer:

\(\displaystyle 132in^3\)

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 9.34.29 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 \(\displaystyle 7\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 3\))

\(\displaystyle 7-3=4\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=3\times4\times7\)   and \(\displaystyle v=4\times3\times4\)

\(\displaystyle v=84in^3\)         and \(\displaystyle v=48in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}84in^3\\ +\ 48in^3\end{array}}{ \ \ \ \space 132in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #311 : Measurement & Data

What is the volume of the figure below? 

Screen shot 2015 12 22 at 9.31.36 am

Possible Answers:

\(\displaystyle 20in^2\)

\(\displaystyle 18in^3\)

\(\displaystyle 48in^3\)

\(\displaystyle 30in^3\)

\(\displaystyle 18in^2\)

Correct answer:

\(\displaystyle 48in^3\)

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 9.32.19 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 \(\displaystyle 5\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 2\))

\(\displaystyle 5-2=3\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=2\times3\times5\)   and \(\displaystyle v=3\times2\times3\)

\(\displaystyle v=30in^3\)         and \(\displaystyle v=18in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}30in^3\\ +\ 18in^3\end{array}}{ \ \ \ \space 48in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #1 : 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 9.47.11 am

Possible Answers:

\(\displaystyle 96in^3\)

\(\displaystyle 75in^3\)

\(\displaystyle 96in^2\)

\(\displaystyle 171in^3\)

\(\displaystyle 75in^2\)

Correct answer:

\(\displaystyle 171in^3\)

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 9.46.50 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 \(\displaystyle 9\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 4\))

\(\displaystyle 9-4=5\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=4\times3\times8\)   and \(\displaystyle v=5\times3\times5\)

\(\displaystyle v=96in^3\)         and \(\displaystyle v=75in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}96in^3\\ +\ 75in^3\end{array}}{ \ \ \space 171in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #2 : 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 9.48.40 am

Possible Answers:

\(\displaystyle 80in^3\)

\(\displaystyle 80in^2\)

\(\displaystyle 270in^3\)

\(\displaystyle 350in^2\)

\(\displaystyle 260in^3\)

Correct answer:

\(\displaystyle 350in^2\)

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 9.48.57 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 \(\displaystyle 10\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 6\))

\(\displaystyle 10-6=4\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=6\times5\times9\)   and \(\displaystyle v=4\times4\times5\)

\(\displaystyle v=270in^3\)         and \(\displaystyle v=80in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}270in^3\\ +\ 80in^3\end{array}}{ \ \ \space 350in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #2 : 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 9.50.01 am

Possible Answers:

\(\displaystyle 600in^3\)

\(\displaystyle 552in^3\)

\(\displaystyle 300in^3\)

\(\displaystyle 252in^3\)

\(\displaystyle 725in^2\)

Correct answer:

\(\displaystyle 552in^3\)

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 9.49.41 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 \(\displaystyle 12\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 6\))

\(\displaystyle 12-6=6\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=6\times5\times10\)   and \(\displaystyle v=6\times6\times7\)

\(\displaystyle v=300in^3\)         and \(\displaystyle v=252in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}300in^3\\ +\ 252in^3\end{array}}{ \ \ \ \space 552in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #4 : 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 9.50.38 am

Possible Answers:

\(\displaystyle 216in^3\)

\(\displaystyle 216in^2\)

\(\displaystyle 361in^3\)

\(\displaystyle 316in^3\)

\(\displaystyle 100in^2\)

Correct answer:

\(\displaystyle 316in^3\)

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 9.50.54 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 \(\displaystyle 11\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 6\))

\(\displaystyle 11-6=5\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=6\times4\times9\)   and \(\displaystyle v=5\times4\times5\)

\(\displaystyle v=216in^3\)         and \(\displaystyle v=100in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}216in^3\\ +\ 100in^3\end{array}}{ \ \ \ \space 316in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #3 : 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 9.51.50 am

Possible Answers:

\(\displaystyle 100in^3\)

\(\displaystyle 512in^3\)

\(\displaystyle 426in^3\)

\(\displaystyle 324in^3\)

\(\displaystyle 432in^3\)

Correct answer:

\(\displaystyle 324in^3\)

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 9.51.28 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 \(\displaystyle 13\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 6\))

\(\displaystyle 13-6=7\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=6\times3\times11\)   and \(\displaystyle v=7\times3\times6\)

\(\displaystyle v=198in^3\)         and \(\displaystyle v=126in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}198in^3\\ +\ 126in^3\end{array}}{ \ \ \ \space 324in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #4 : 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 9.54.53 am

Possible Answers:

\(\displaystyle 640in^3\)

\(\displaystyle 520in^3\)

\(\displaystyle 120in^3\)

\(\displaystyle 400in^3\)

\(\displaystyle 280in^3\)

Correct answer:

\(\displaystyle 400in^3\)

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 9.55.09 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 \(\displaystyle 13\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 7\))

\(\displaystyle 13-7=6\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=7\times4\times10\)   and \(\displaystyle v=6\times4\times5\)

\(\displaystyle v=280in^3\)         and \(\displaystyle v=120in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}280in^3\\ +\ 120in^3\end{array}}{ \ \ \ \space 400in^3}\)

*Remember, volume is always measured in cubic units! 

Example Question #5 : 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 9.55.46 am

Possible Answers:

\(\displaystyle 352in^3\)

\(\displaystyle 492in^3\)

\(\displaystyle 140in^3\)

\(\displaystyle 280in^3\)

\(\displaystyle 600in^3\)

Correct answer:

\(\displaystyle 492in^3\)

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 9.55.29 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 \(\displaystyle 15\)) and subtract the length of the rectangular prism on the left (which is \(\displaystyle 8\))

\(\displaystyle 15-8=7\)

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

Remember, the formula for volume is 

\(\displaystyle v=l\times w\times h\)

\(\displaystyle v=8\times4\times11\)   and \(\displaystyle v=7\times4\times5\)

\(\displaystyle v=352in^3\)         and \(\displaystyle v=140in^3\)

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

\(\displaystyle \frac{\begin{array}[b]{r}352in^3\\ +\ 140in^3\end{array}}{ \ \ \ \space 492in^3}\)

*Remember, volume is always measured in cubic units! 

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