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Common Core: 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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Example Questions

Example Question #1 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

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.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

V = LWH $\displaystyle V = LWH$

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

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

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

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

Which is the greater quantity?

(A) The volume of a rectangular solid ten inches by twenty inches by fifteen inches

(B) The volume of a cube with sidelength sixteen inches

Possible Answers:

It is impossible to determine which is greater from the information given

(B) is greater

(A) and (B) are equal

(A) is greater

Correct answer:

(B) is greater

Explanation:

The volume of a rectangular solid ten inches by twenty inches by fifteen inches is

$V = 10 \cdot 20 \cdot15 = 3,000$ $\displaystyle V = 10 \cdot 20 \cdot15 = 3,000$ cubic inches.

The volume of a cube with sidelength 13 inches is

$V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ $\displaystyle V = 16^{3} = 16 \cdot 16 \cdot 16 = 4,096$ cubic inches.

This makes (B) greater

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Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A prism with a square base has a height of $\displaystyle 4$ feet.

If the edge of the base is $\displaystyle 2$ feet, what is the volume of the prism?

Possible Answers:

$4\, ft^3$ $\displaystyle 4\, ft^3$

$16\, ft^3$ $\displaystyle 16\, ft^3$

$8\, ft^3$ $\displaystyle 8\, ft^3$

$6\, ft^3$ $\displaystyle 6\, ft^3$

Correct answer:

$16\, ft^3$ $\displaystyle 16\, ft^3$

Explanation:

The volume of a prism is given as

V = Bh $\displaystyle V = Bh$

where

B = Area of the base

and

h = height of the prism.

Because the base is a square, we have

$\displaystyle B = s^2 = 2^2 = 4$

So plugging in the value of B that we found and h that was given in the problem we get the volume to be the following.

$V = 4\cdot4 = 16\,ft^3$ $\displaystyle V = 4\cdot4 = 16\,ft^3$

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Example Question #22 : Prisms

A rectangular prism has the dimensions of $2\:in$ $\displaystyle 2\:in$, $5\:in$ $\displaystyle 5\:in$, and $7\:in$ $\displaystyle 7\:in$. What is the volume of the prism?

Possible Answers:

$63 \:in^2$ $\displaystyle 63 \:in^2$

$70\:in^2$ $\displaystyle 70\:in^2$

$63\: in^3$ $\displaystyle 63\: in^3$

$72\:in^3$ $\displaystyle 72\:in^3$

$70\:in^3$ $\displaystyle 70\:in^3$

Correct answer:

$70\:in^3$ $\displaystyle 70\:in^3$

Explanation:

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$ $\displaystyle V= l \cdot w \cdot h$

In this equation, $\displaystyle l$ is length, $\displaystyle w$ is width, and $\displaystyle h$ is height.

The given information does not explicitly state which side each dimension measurement correlates to on the prism. Volume simply requires the multiplication of the dimensions together.

Volume can be solved for in the following way:

$V = 2\:in \cdot 5\:in \cdot 7\:in$ $\displaystyle V = 2\:in \cdot 5\:in \cdot 7\:in$

$V = 10\:in^2 \cdot 7\:in$ $\displaystyle V = 10\:in^2 \cdot 7\:in$

$V= 70 \:in^3$ $\displaystyle V= 70 \:in^3$

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Example Question #4 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Find the volume of a rectangular prism with a width of $2\:cm$ $\displaystyle 2\:cm$, height of $8\:cm$ $\displaystyle 8\:cm$ and length of $3\:cm$ $\displaystyle 3\:cm$.

Possible Answers:

$24\:cm^3$ $\displaystyle 24\:cm^3$

$56\:cm^3$ $\displaystyle 56\:cm^3$

$26\:cm^3$ $\displaystyle 26\:cm^3$

$48\:cm^3$ $\displaystyle 48\:cm^3$

$58\:cm^3$ $\displaystyle 58\:cm^3$

Correct answer:

$48\:cm^3$ $\displaystyle 48\:cm^3$

Explanation:

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$ $\displaystyle V= l \cdot w \cdot h$

In this equation, $\displaystyle l$ is length, $\displaystyle w$ is width, and $\displaystyle h$ is height.

Because all the necessary information has been provided to solve for the volume, all that needs to be done is substituting in the values for the variables.

Therefore:

$V = 2\:cm \cdot 3\:cm \cdot 8\:cm$ $\displaystyle V = 2\:cm \cdot 3\:cm \cdot 8\:cm$

$V = 6\:cm^2 \cdot 8\:cm$ $\displaystyle V = 6\:cm^2 \cdot 8\:cm$

$V = 48\:cm^3$ $\displaystyle V = 48\:cm^3$

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Example Question #61 : Geometry

Find the surface area of the rectangular prism:

Volume_of_a_prism

Possible Answers:

$468\:units^3$ $\displaystyle 468\:units^3$

$418\:units^3$ $\displaystyle 418\:units^3$

$468\:units^2$ $\displaystyle 468\:units^2$

$410\:units^2$ $\displaystyle 410\:units^2$

$453\:units^3$ $\displaystyle 453\:units^3$

Correct answer:

$410\:units^2$ $\displaystyle 410\:units^2$

Explanation:

The surface area of a rectangular prism is

$\displaystyle SA=2lw+2lh+2wh$

Substituting in the given information for this particular rectangular prism.

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

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Example Question #5 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A small rectangular fish tank has sides that are 18in $\displaystyle 18in$ wide, 30in $\displaystyle 30in$ long, and 24in $\displaystyle 24in$ high. Which formula would not work to find the correct volume of the fish tank?

Possible Answers:

$720 \times 18$ $\displaystyle 720 \times 18$

$(18 \times 30) + 24$ $\displaystyle (18 \times 30) + 24$

$(30 \times 24) \times 18$ $\displaystyle (30 \times 24) \times 18$

$(24 \times 18) \times 30$ $\displaystyle (24 \times 18) \times 30$

$30 \times 432$ $\displaystyle 30 \times 432$

Correct answer:

$(18 \times 30) + 24$ $\displaystyle (18 \times 30) + 24$

Explanation:

In this question the formula that uses addition will not yield the correct volume of the fish tank:

$\displaystyle (18 x 30) + 24$

This is the correct answer because in order to find the volume of any rectangular prism one needs to multiply the prism's length, width, and height together.

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$ $\displaystyle V= l \cdot w \cdot h$

In this equation, $\displaystyle l$ is length, $\displaystyle w$ is width, and $\displaystyle h$ is height.

To restate, $\displaystyle (18 x 30) + 24$ is the correct answer because it will NOT yield the correct volume, you would need to multiply $\displaystyle 24$ by the product of $\displaystyle 18$ and $\displaystyle 30$, not add.

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Example Question #1235 : Grade 6

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

Possible Answers:

$159\textup{ cm}^3$ $\displaystyle 159\textup{ cm}^3$

$156\textup{ cm}^3$ $\displaystyle 156\textup{ cm}^3$

$160.5\textup{ cm}^3$ $\displaystyle 160.5\textup{ cm}^3$

$158.5\textup{ cm}^3$ $\displaystyle 158.5\textup{ cm}^3$

$166\textup{ cm}^3$ $\displaystyle 166\textup{ cm}^3$

Correct answer:

$156\textup{ cm}^3$ $\displaystyle 156\textup{ cm}^3$

Explanation:

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

$A=l\times w\times h$ $\displaystyle A=l\times w\times h$

Substitute our side lengths:

$A=6\frac{1}{2}\times3\times8$ $\displaystyle A=6\frac{1}{2}\times3\times8$

$A=156\textup{ cm}^3$ $\displaystyle A=156\textup{ cm}^3$

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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Example Question #1 : 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?

Possible Answers:

$136.5\textup{ cm}^3$ $\displaystyle 136.5\textup{ cm}^3$

$142\textup{ cm}^3$ $\displaystyle 142\textup{ cm}^3$

$138.5\textup{ cm}^3$ $\displaystyle 138.5\textup{ cm}^3$

$147.5\textup{ cm}^3$ $\displaystyle 147.5\textup{ cm}^3$

$140\textup{ cm}^3$ $\displaystyle 140\textup{ cm}^3$

Correct answer:

$136.5\textup{ cm}^3$ $\displaystyle 136.5\textup{ cm}^3$

Explanation:

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

$A=l\times w\times h$ $\displaystyle A=l\times w\times h$

Substitute our side lengths:

$A=6\frac{1}{2}\times3\times7$ $\displaystyle A=6\frac{1}{2}\times3\times7$

$A=136.5\textup{ cm}^3$ $\displaystyle A=136.5\textup{ cm}^3$

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

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Example Question #6 : 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?

Possible Answers:

$175.5\textup{ cm}^3$ $\displaystyle 175.5\textup{ cm}^3$

$180\textup{ cm}^3$ $\displaystyle 180\textup{ cm}^3$

$185.5\textup{ cm}^3$ $\displaystyle 185.5\textup{ cm}^3$

$183\textup{ cm}^3$ $\displaystyle 183\textup{ cm}^3$

$190\textup{ cm}^3$ $\displaystyle 190\textup{ cm}^3$

Correct answer:

$175.5\textup{ cm}^3$ $\displaystyle 175.5\textup{ cm}^3$

Explanation:

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

$A=l\times w\times h$ $\displaystyle A=l\times w\times h$

Substitute our side lengths:

$A=6\frac{1}{2}\times3\times9$ $\displaystyle A=6\frac{1}{2}\times3\times9$

$A=175.5\textup{ cm}^3$ $\displaystyle A=175.5\textup{ cm}^3$

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

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

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

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #1 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

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

Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #22 : Prisms

Example Question #4 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #61 : Geometry

Example Question #5 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #1235 : Grade 6

Example Question #1 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

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

All Common Core: 6th Grade Math Resources

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