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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 Question #1 : Solid Geometry

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:

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

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

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

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

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

Correct answer:

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

Explanation:

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

V = LWH

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

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

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

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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

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:

(A) and (B) are equal

(B) is greater

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

(A) is greater

Correct answer:

(B) is greater

Explanation:

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

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

The volume of a cube with sidelength 13 inches is

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

This makes (B) greater

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Example Question #61 : Geometry

A prism with a square base has a height of feet.

If the edge of the base is feet, what is the volume of the prism?

Possible Answers:

$8\, ft^3$

$16\, ft^3$

$6\, ft^3$

$4\, ft^3$

Correct answer:

$16\, ft^3$

Explanation:

The volume of a prism is given as

V = Bh

where

B = Area of the base

and

h = height of the prism.

Because the base is a square, we have

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.

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

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Example Question #1 : How To Find The Volume Of A Prism

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

Possible Answers:

$70\:in^2$

$72\:in^3$

$63\: in^3$

$63 \:in^2$

$70\:in^3$

Correct answer:

$70\:in^3$

Explanation:

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

$V= l \cdot w \cdot h$

In this equation, is length, is width, and 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:

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

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

$V= 70 \:in^3$

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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

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

Possible Answers:

$48\:cm^3$

$26\:cm^3$

$58\:cm^3$

$24\:cm^3$

$56\:cm^3$

Correct answer:

$48\:cm^3$

Explanation:

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

$V= l \cdot w \cdot h$

In this equation, is length, is width, and 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:

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

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

$V = 48\:cm^3$

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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

Find the surface area of the rectangular prism:

Volume_of_a_prism

Possible Answers:

$468\:units^3$

$453\:units^3$

$410\:units^2$

$468\:units^2$

$418\:units^3$

Correct answer:

$410\:units^2$

Explanation:

The surface area of a rectangular prism is

SA=2lw+2lh+2wh

Substituting in the given information for this particular rectangular prism.

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

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Example Question #1 : How To Find The Volume Of A Prism

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

Possible Answers:

$(30 \times 24) \times 18$

$(18 \times 30) + 24$

$720 \times 18$

$(24 \times 18) \times 30$

$30 \times 432$

Correct answer:

$(18 \times 30) + 24$

Explanation:

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

(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:

$V= l \cdot w \cdot h$

In this equation, is length, is width, and is height.

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

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Example Question #8 : 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:

$160.5\textup{ cm}^3$

$158.5\textup{ cm}^3$

$156\textup{ cm}^3$

$159\textup{ cm}^3$

$166\textup{ cm}^3$

Correct answer:

$156\textup{ cm}^3$

Explanation:

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

$A=l\times w\times h$

Substitute our side lengths:

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

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

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:

$147.5\textup{ cm}^3$

$142\textup{ cm}^3$

$140\textup{ cm}^3$

$138.5\textup{ cm}^3$

$136.5\textup{ cm}^3$

Correct answer:

$136.5\textup{ cm}^3$

Explanation:

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

$A=l\times w\times h$

Substitute our side lengths:

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

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

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 #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:

$183\textup{ cm}^3$

$175.5\textup{ cm}^3$

$185.5\textup{ cm}^3$

$180\textup{ cm}^3$

$190\textup{ cm}^3$

Correct answer:

$175.5\textup{ cm}^3$

Explanation:

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

$A=l\times w\times h$

Substitute our side lengths:

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

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

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 : Solid Geometry

Example Question #1 : 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 #1 : How To Find The Volume Of A Prism

Example Question #5 : 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 #1 : How To Find The Volume Of A Prism

Example Question #8 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

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

Example Question #1 : 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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