Find the Volume of a Right Rectangular Prism with Fractional Edge Lengths: CCSS.Math.Content.6.G.A.2

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6th Grade Math › Find the Volume of a Right Rectangular Prism with Fractional Edge Lengths: CCSS.Math.Content.6.G.A.2

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A large crate in the shape of a rectangular prism has dimensions 5 feet by 4 feet by 12 feet. Give its volume in cubic yards.

$8 \frac{8}{9 } \textrm{ yd}^{3}$

$7 \frac{2}{9 } \textrm{ yd}^{3}$

$10 \textrm{ yd}^{3}$

$80 \textrm{ yd}^{3}$

$90\textrm{ yd}^{3}$

Explanation

Divide each dimension by 3 to convert feet to yards, then multiply the three dimensions together:

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{12}{3}$

$V = \frac{5}{3} \cdot \frac{4}{3} \cdot \frac{4}{1}$

$V = \frac{80}{9 } = 8 \frac{8}{9 } \textrm{ yd}^{3}$

Find the surface area of the rectangular prism:

Volume_of_a_prism

Explanation

The surface area of a rectangular prism is

Substituting in the given information for this particular rectangular prism.

$\SA=2(13\cdot 9)+2(13\cdot 4)+2(9\cdot 4) \SA=410\ \text{units}^2$

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

$65.25\textup{ cm}^3$

$63.25\textup{ cm}^3$

$66\textup{ cm}^3$

$67.75\textup{ cm}^3$

$68.5\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=7\frac{1}{4}\times3\times3$

$A=65.25\textup{ cm}^3$

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

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

$98\textup{ cm}^3$

$97\textup{ cm}^3$

$100\textup{ cm}^3$

$103.5\textup{ cm}^3$

$105\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=3\frac{1}{2}\times4\times7$

$A=98\textup{ cm}^3$

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

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

$47.25\textup{ cm}^3$

$45\textup{ cm}^3$

$49\textup{ cm}^3$

$51.25\textup{ cm}^3$

$53.5\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=5\frac{1}{4}\times3\times3$

$A=47.25\textup{ cm}^3$

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

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

$36\textup{ cm}^3$

$37\textup{ cm}^3$

$35.5\textup{ cm}^3$

$34\textup{ cm}^3$

$32\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=4\frac{1}{2}\times4\times2$

$A=36\textup{ cm}^3$

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

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

$150\textup{ cm}^3$

$151\textup{ cm}^3$

$152\textup{ cm}^3$

$149.5\textup{ cm}^3$

$148.5\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=7\frac{1}{2}\times4\times5$

$A=150\textup{ cm}^3$

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

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

$49.5\textup{ cm}^3$

$50\textup{ cm}^3$

$48.25\textup{ cm}^3$

$47.5\textup{ cm}^3$

$45\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=8\frac{1}{4}\times3\times2$

$A=49.5\textup{ cm}^3$

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

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

$87\textup{ cm}^3$

$86.26\textup{ cm}^3$

$88.5\textup{ cm}^3$

$90.5\textup{ cm}^3$

$89.25\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=7\frac{1}{4}\times3\times4$

$A=87\textup{ cm}^3$

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

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

$173.25\textup{ cm}^3$

$172.25\textup{ cm}^3$

$171.5\textup{ cm}^3$

$170.75\textup{ cm}^3$

$175.5\textup{ cm}^3$

Explanation

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

$A=l\times w\times h$

Substitute our side lengths:

$A=8\frac{1}{4}\times3\times7$

$A=173.25\textup{ cm}^3$

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

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