Common Core: 6th Grade Math : Geometry

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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Example Questions

Example Question #1280 : Grade 6

What is the volume of the rectangular prism in the following figure?

2

Possible Answers:

\(\displaystyle 53.5\textup{ cm}^3\)

\(\displaystyle 45\textup{ cm}^3\)

\(\displaystyle 49\textup{ cm}^3\)

\(\displaystyle 51.25\textup{ cm}^3\)

\(\displaystyle 47.25\textup{ cm}^3\)

Correct answer:

\(\displaystyle 47.25\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=5\frac{1}{4}\times3\times3\)

\(\displaystyle A=47.25\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #111 : Geometry

What is the volume of the rectangular prism in the following figure?

3

Possible Answers:

\(\displaystyle 63\textup{ cm}^3\)

\(\displaystyle 61\textup{ cm}^3\)

\(\displaystyle 64.5\textup{ cm}^3\)

\(\displaystyle 69.5\textup{ cm}^3\)

\(\displaystyle 66\textup{ cm}^3\)

Correct answer:

\(\displaystyle 63\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=5\frac{1}{4}\times3\times4\)

\(\displaystyle A=63\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #112 : Geometry

What is the volume of the rectangular prism in the following figure?

4

Possible Answers:

\(\displaystyle 80\textup{ cm}^3\)

\(\displaystyle 75.25\textup{ cm}^3\)

\(\displaystyle 78.75\textup{ cm}^3\)

\(\displaystyle 79.5\textup{ cm}^3\)

\(\displaystyle 82.25\textup{ cm}^3\)

Correct answer:

\(\displaystyle 78.75\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=5\frac{1}{4}\times3\times5\)

\(\displaystyle A=78.75\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #113 : Geometry

What is the volume of the rectangular prism in the following figure?

5

Possible Answers:

\(\displaystyle 96.75\textup{ cm}^3\)

\(\displaystyle 92.5\textup{ cm}^3\)

\(\displaystyle 98.25\textup{ cm}^3\)

\(\displaystyle 94.5\textup{ cm}^3\)

\(\displaystyle 100\textup{ cm}^3\)

Correct answer:

\(\displaystyle 94.5\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=5\frac{1}{4}\times3\times6\)

\(\displaystyle A=94.5\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #114 : Geometry

What is the volume of the rectangular prism in the following figure?

6

Possible Answers:

\(\displaystyle 110.25\textup{ cm}^3\)

\(\displaystyle 118.5\textup{ cm}^3\)

\(\displaystyle 120.75\textup{ cm}^3\)

\(\displaystyle 115.75\textup{ cm}^3\)

\(\displaystyle 105.5\textup{ cm}^3\)

Correct answer:

\(\displaystyle 110.25\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=5\frac{1}{4}\times3\times7\)

\(\displaystyle A=110.25\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #115 : Geometry

What is the volume of the rectangular prism in the following figure?

1

Possible Answers:

\(\displaystyle 47.5\textup{ cm}^3\)

\(\displaystyle 43.5\textup{ cm}^3\)

\(\displaystyle 45.5\textup{ cm}^3\)

\(\displaystyle 40\textup{ cm}^3\)

\(\displaystyle 44.25\textup{ cm}^3\)

Correct answer:

\(\displaystyle 45.5\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=3\frac{1}{4}\times2\times7\)

\(\displaystyle A=45.5\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #51 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

What is the volume of the rectangular prism in the following figure?

2

Possible Answers:

\(\displaystyle 36\textup{ cm}^3\)

\(\displaystyle 35.75\textup{ cm}^3\)

\(\displaystyle 39\textup{ cm}^3\)

\(\displaystyle 38.25\textup{ cm}^3\)

\(\displaystyle 40.5\textup{ cm}^3\)

Correct answer:

\(\displaystyle 39\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=3\frac{1}{4}\times2\times6\)

\(\displaystyle A=39\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #117 : Geometry

What is the volume of the rectangular prism in the following figure?

3

Possible Answers:

\(\displaystyle 54\textup{ cm}^3\)

\(\displaystyle 55.25\textup{ cm}^3\)

\(\displaystyle 56\textup{ cm}^3\)

\(\displaystyle 60\textup{ cm}^3\)

\(\displaystyle 58.5\textup{ cm}^3\)

Correct answer:

\(\displaystyle 58.5\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=3\frac{1}{4}\times2\times9\)

\(\displaystyle A=58.5\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #118 : Geometry

What is the volume of the rectangular prism in the following figure?

5

Possible Answers:

\(\displaystyle 33.25\textup{ cm}^3\)

\(\displaystyle 31.5\textup{ cm}^3\)

\(\displaystyle 32.5\textup{ cm}^3\)

\(\displaystyle 30.75\textup{ cm}^3\)

\(\displaystyle 31.25\textup{ cm}^3\)

Correct answer:

\(\displaystyle 32.5\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=3\frac{1}{4}\times2\times5\)

\(\displaystyle A=32.5\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

Example Question #119 : Geometry

What is the volume of the rectangular prism in the following figure?

6

Possible Answers:

\(\displaystyle 49.25\textup{ cm}^3\)

\(\displaystyle 53\textup{ cm}^3\)

\(\displaystyle 50.5\textup{ cm}^3\)

\(\displaystyle 48.75\textup{ cm}^3\)

\(\displaystyle 52\textup{ cm}^3\)

Correct answer:

\(\displaystyle 52\textup{ cm}^3\)

Explanation:

The formula used to find volume of a rectangular prism is as follows:

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

Substitute our side lengths:

\(\displaystyle A=3\frac{1}{4}\times2\times8\)

\(\displaystyle A=52\textup{ cm}^3\)

Remember, volume is always written with cubic units because volume is how many cubic units can fit inside of a figure.

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