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SSAT Upper Level Math : Geometry

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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:

$11\textup{ units}^3$

$10\textup{ units}^3$

$8\textup{ units}^3$

$14\textup{ units}^3$

$12\textup{ units}^3$

Correct answer:

$12\textup{ units}^3$

Explanation:

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

$4\times3=12$

$v=12\ units^3$

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

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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:

$8\textup{ units}^3$

$10\textup{ units}^3$

$9\textup{ units}^3$

$7\textup{ units}^3$

$11\textup{ units}^3$

Correct answer:

$8\textup{ units}^3$

Explanation:

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

$4\times2=8$

$v=8\ units^3$

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

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Example Question #711 : Geometry

Box

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

Possible Answers:

500

200

2,000

1,000

Correct answer:

2,000

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:

$V = LWH = 20 \cdot 10 \cdot 10 = 2,000$ .

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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:

$2x^{2} + 120$

120x+1,800

$30x^{2}$

900x

Correct answer:

$30x^{2}$

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

$V = 30 \cdot x \cdot x = 30x ^{2}$ .

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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.

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

A given right rectangular pyramid has a base length and base width of $60\:m$ , as well as a height of $70\:m$ . What is the volume of the pyramid?

Possible Answers:

$84000\:m^{3}$

Not enough information provided

$252,000\:m^{3}$

$364,500\:m^{3}$

$124,000\:m^3$

Correct answer:

$84000\:m^{3}$

Explanation:

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

$V=\frac{lwh}{3}$ .

Plugging in our given values for each variable, we have

$V=\frac{60\:m\times 60\:m\times 70\:m}{3}$

$V=\frac{252000\:m^{3}}{3}$

$V=84000\:m^{3}$

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

A given right rectangular pyramid has a base length of $100\:m$ , a base width of $50\:m$ , and a height of $75\:m$ . What is the volume of the pyramid?

Possible Answers:

$225\:m^{3}$

$375,000\:m^{2}$

$125,000\:m^{3}$

$125,000\:m^{2}$

$375,000\:m^{3}$

Correct answer:

$125,000\:m^{3}$

Explanation:

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

$V=\frac{lwh}{3}$ .

Plugging in our given values for each variable, we have

$V=\frac{100\:m\times 50\:m\times 75\:m}{3}$

$V=\frac{375000\:m^{3}}{3}$

$V=125000\:m^{3}$

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

A given rectangular pyramid has a base length of $5\:m$ , a base width of $3\:m$ , and a height of $7\:m$ . What is the volume of the pyramid?

Possible Answers:

$35\:m^{3}$

$124\:m^3$

Cannot be determined with the information provided

$72\:m^3$

$105\:m^{3}$

Correct answer:

$35\:m^{3}$

Explanation:

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

$V=\frac{lwh}{3}$ .

Plugging in our given values for each variable, we have

$V=\frac{5\:m\times 3\:m\times 7\:m}{3}$

In this instance, since we have a in both the numerator and the denominator, we can reduce the formula to:

$V=5\:m\times1\:m\times7\:m$

$V=35\:m^{3}$

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Example Question #4 : How To Find The Volume Of A Pyramid

A rectangular pyramid has a width of , a height of , and a length of . What is the volume of this pyramid, in cubic meters?

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

Since we have a rectangular pyramid, the base of the pyramid is a rectangle. Find the area of the rectangle.

$\text{Area}=\text{length}\times\text{width}$

$\text{Area}=4\times3=12$

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

$\text{Volume}=\frac{12\times7}{3}=\frac{84}{3}=28$

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

A rectangular pyramid has a length of 12m , a width of , and a height of . In cubic meters, what is the volume?

Possible Answers:

240

120

160

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

Since we have a rectangular pyramid, the base of the pyramid is a rectangle. Find the area of the rectangle.

$\text{Area}=\text{length}\times\text{width}$

$\text{Area}=12\times4=48$

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

$\text{Volume}=\frac{48\times5}{3}=\frac{240}{3}=80$

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SSAT Upper Level Math : Geometry

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

All SSAT Upper Level Math Resources

Example Questions

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

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

Example Question #711 : Geometry

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

Example Question #51 : Measurement & Data

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

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

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

Example Question #4 : How To Find The Volume Of A Pyramid

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

All SSAT Upper Level Math Resources

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