SSAT Upper Level Math : Volume of a Three-Dimensional Figure

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #91 : Volume Of A Three Dimensional Figure

Can we determine the volume of this shape? 

Screen shot 2015 07 29 at 10.56.45 am

Possible Answers:

No because this shape is flat

Yes because this is a closed shape 

Yes because we know each of the side lengths

No because this shape does not provide enough information to find the volume

Correct answer:

No because this shape is flat

Explanation:

Volume is only a characteristic of three-dimensional shapes. We can think of volume as space within an object or shape.  Because this is a flat shape, it does not have a volume.

Example Question #61 : Measurement & Data

Can we determine the volume of this shape? 

Screen shot 2015 07 29 at 10.58.34 am

Possible Answers:

No because this shape is flat

Yes because this shape is a perfect square

No because this shape is open

Yes because we know all the side lengths 

Correct answer:

No because this shape is flat

Explanation:

Volume is only a characteristic of three-dimensional shapes. We can think of volume as space within an object or shape.  Because this is a flat shape, it does not have a volume.

Example Question #62 : Measurement & Data

Can we determine the volume of this shape? 

Screen shot 2015 07 29 at 11.08.14 am

Possible Answers:

No because we were not given the area

Yes because this is a three-dimensional shape

No because this shape is flat

Yes because we are given the width 

Correct answer:

Yes because this is a three-dimensional shape

Explanation:

Volume is a characteristic of three-dimensional shapes. This is a cube, which is a three-dimensional shape. We can think of volume as space within an object or shape, so the volume would be the amount of space inside this cube. 

Example Question #932 : Ssat Upper Level Quantitative (Math)

 What is the volume of the object below? 

Screen shot 2015 07 29 at 8.34.50 am

Possible Answers:

Correct answer:

Explanation:

This object has  rows with  cubes in each row. We can multiply to find the volume. 

Remember, volume is always labeled as units to the third power. 

Example Question #31 : How To Find The Volume Of A Prism

 What is the volume of the object below? 


Screen shot 2015 07 29 at 8.31.38 am

Possible Answers:

Correct answer:

Explanation:

This object has  rows with  cubes in each row. We can multiply to find the volume. 

Remember, volume is always labeled as units to the third power. 

Example Question #92 : Volume Of A Three Dimensional Figure

Box

The above diagram shows a rectangular solid. The shaded side is a square. Give the volume of the solid.

Possible Answers:

Correct answer:

Explanation:

A square has four sides of equal length, so, as seen in the diagram below, the length, width, and height of the solid are 20, 10, and 10.

Box 3

The volume of the solid is the product of the three dimensions:

.

Example Question #42 : How To Find The Volume Of A Prism

Box

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the volume of the solid.

Possible Answers:

Correct answer:

Explanation:

The volume of a rectangular solid is the product of its three dimensions. Since the left (and right) surfaces are squares, as seen in the figure below, the missing dimension is equal to .

Untitled 4

The dimensions are 30, , and , making the volume

.

Example Question #51 : Measurement & Data

Can we determine the volume of this shape?

Screen shot 2015 07 29 at 10.55.06 am

Possible Answers:

Yes because we are given all of the side lengths 

No because this shape only has three sides

No because this shape is flat

Yes because this is a closed shape

Correct answer:

No because this shape is flat

Explanation:

Volume is only a characteristic of three-dimensional shapes. We can think of volume as space within an object or shape.  Because this is a flat shape, it does not have a volume.

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

A given right rectangular pyramid has a base length and base width of , as well as a height of . What is the volume of the pyramid?

Possible Answers:

Not enough information provided

Correct answer:

Explanation:

The volume  of a right rectangular pyramid with base length , base width , and height  can be determined with the following formula:

.

Plugging in our given values for each variable, we have

Example Question #2 : How To Find The Volume Of A Pyramid

A given right rectangular pyramid has a base length of , a base width of , and a height of . What is the volume of the pyramid?

Possible Answers:

Correct answer:

Explanation:

The volume  of a right rectangular pyramid with base length , base width , and height  can be determined with the following formula:

.

Plugging in our given values for each variable, we have

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