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

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Question

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.

Answer

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

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

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

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

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Question

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

Answer

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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Question

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?

Answer

The volume of a prism is given as

where

B = Area of the base

and

h = height of the prism.

Because the base is a square, we have

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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Question

Find the surface area of the rectangular prism:

Answer

The surface area of a rectangular prism is

Substituting in the given information for this particular rectangular prism.

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

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Question

Find the volume of a rectangular prism with a width of , height of and length of .

Answer

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:

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

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

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Question

A rectangular prism has the dimensions of , , and . What is the volume of the prism?

Answer

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:

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

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

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Question

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

Answer

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

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, 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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=6\frac{1}{2}\times3\times10$

$A=195\textup{ cm}^3$

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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Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=6\frac{1}{2}\times3\times11$

$A=214.5\textup{ cm}^3$

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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Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=6\frac{1}{2}\times3\times12$

$A=234\textup{ cm}^3$

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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Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=5\frac{1}{2}\times4\times7$

$A=154\textup{ cm}^3$

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

Compare your answer with the correct one above

Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=5\frac{1}{2}\times4\times6$

$A=132\textup{ cm}^3$

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

Compare your answer with the correct one above

Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=5\frac{1}{2}\times4\times8$

$A=176\textup{ cm}^3$

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

Compare your answer with the correct one above

Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=5\frac{1}{2}\times4\times9$

$A=198\textup{ cm}^3$

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

Compare your answer with the correct one above

Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=5\frac{1}{2}\times4\times10$

$A=220\textup{ cm}^3$

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

Compare your answer with the correct one above

Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=5\frac{1}{2}\times4\times11$

$A=242\textup{ cm}^3$

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

Compare your answer with the correct one above

Question

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

Answer

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

$A=l\times w\times h$

Substitute our side lengths:

$A=3\frac{1}{2}\times4\times11$

$A=154\textup{ cm}^3$

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

Compare your answer with the correct one above

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