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SSAT Upper Level Math : Geometry

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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 #6 : How To Find The Volume Of A Pyramid

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

Possible Answers:

256

384

336

128

Correct answer:

128

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.

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

$\text{Area}=4\times8=32$

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.

$\text{Volume}=\frac{32\times12}{3}=\frac{384}{3}=128$

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Example Question #7 : How To Find The Volume Of A Pyramid

A pyramid has a square base with a side length of and a height of 12m . In cubic meters, find the volume.

Possible Answers:

392

556

588

196

Correct answer:

196

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 square pyramid, the base of the pyramid is a square. Find the area of the square.

$\text{Area}=\text{length}^2$

$\text{Area}=7^2=49$

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.

$\text{Volume}=\frac{49\times12}{3}=\frac{588}{3}=196$

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

A pyramid with a square base that has a side length of 12m has a height of . In cubic meters, find the volume.

Possible Answers:

480

240

720

960

Correct answer:

240

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 square pyramid, the base of the pyramid is a square. Find the area of the square.

$\text{Area}=\text{length}^2$

$\text{Area}=12^2=144$

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.

$\text{Volume}=\frac{144\times4}{3}=\frac{720}{3}=240$

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Example Question #8 : How To Find The Volume Of A Pyramid

A pyramid with a square base that has a side length of has a height of . In cubic meters, what is the volume of the pyramid?

Possible Answers:

320

960

500

640

Correct answer:

320

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 square pyramid, the base of the pyramid is a square. Find the area of the square.

$\text{Area}=\text{length}^2$

$\text{Area}=8^2=64$

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.

$\text{Volume}=\frac{64\times15}{3}=\frac{960}{3}=320$

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Example Question #3 : How To Find The Volume Of A Pyramid

A pyramid has a square base of side and a height of 11m . Find the volume of the pyramid in cubic meters.

Possible Answers:

132

264

396

256

Correct answer:

132

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 square pyramid, the base of the pyramid is a square. Find the area of the square.

$\text{Area}=\text{length}^2$

$\text{Area}=6^2=36$

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.

$\text{Volume}=\frac{36\times11}{3}=\frac{396}{3}=132$

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Example Question #721 : Geometry

A pyramid has a square base of side and a height of 12m . In cubic meters, find the volume of the pyramid.

Possible Answers:

300

400

100

200

Correct answer:

100

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 square pyramid, the base of the pyramid is a square. Find the area of the square.

$\text{Area}=\text{length}^2$

$\text{Area}=5^2=25$

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.

$\text{Volume}=\frac{25\times12}{3}=\frac{300}{3}=100$

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Example Question #722 : Geometry

A rectangular pyramid has a length of 15m , a width of , and a height of . In cubic meters, find the volume.

Possible Answers:

420

360

280

140

Correct answer:

140

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.

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

$\text{Area}=15\times7=105$

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.

$\text{Volume}=\frac{105\times4}{3}=\frac{420}{3}=140$

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Example Question #111 : Volume Of A Three Dimensional Figure

The height of a cylinder is 3 inches and the radius of the circular end of the cylinder is 3 inches. Give the volume and surface area of the cylinder.

Possible Answers:

V=74.78 in^3, A=103.04in^2

V=84.78 in^3, A=123.04in^2

V=74.78 in^3, A=113.10in^2

V=84.78 in^3, A=103.04in^2

V=84.82 in^3, A=113.10in^2

Correct answer:

V=84.82 in^3, A=113.10in^2

Explanation:

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height or:

$Volume=\pi r^2h$

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

$Volume=\pi r^2h=\pi \times 3^2\times 3=84.82in^3$

The surface area of the cylinder is given by:

$A=2\pi r^2+2\pi rh$

where is the surface area of the cylinder, is the radius of the cylinder and is the height of the cylinder. So we can write:

$A=2\pi r^2+2\pi rh$

$A=2\pi (3)^2+2\pi \times 3\times 3$

$A=18\pi+18\pi$

$A=36\pi$

A=113.10

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

The height of a cylinder is two times the length of the radius of the circular end of a cylinder. If the volume of the cylinder is $16\pi$ , what is the height of the cylinder?

Possible Answers:

$2\sqrt{2}$

Correct answer:

Explanation:

The volume of a cylinder is:

$Volume=\pi r^2h$

where is the radius of the circular end of the cylinder and is the height of the cylinder.

Since h=2r , we can substitute that into the volume formula. So we can write:

$Volume=\pi r^2h$

$16\pi=\pi r^2\cdot (2r)$

$16\pi =2\pi r^{3}$

$16=2r^{3}$

$8=r^{3}$

r=2

So we get:

$h=2r=2\times 2=4$

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

The end (base) of a cylinder has an area of $16\pi$ square inches. If the height of the cylinder is half of the radius of the base of the cylinder, give the volume of the cylinder.

Possible Answers:

$8\pi$

$16\pi$

$32\pi$

Correct answer:

$32\pi$

Explanation:

The area of the end (base) of a cylinder is $\pi r^2$ , so we can write:

$\pi r^2=16\pi\Rightarrow r^2=16\Rightarrow r=4\ inches$

The height of the cylinder is half of the radius of the base of the cylinder, that means:

$h=\frac{r}{2}=\frac{4}{2}=2\ inches$

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height:

$Volume=Area\times h=16\pi\times 2=32\pi$

$Volume=\pi r^2h=\pi\times 4^2\times 2=32\pi$

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All SSAT Upper Level Math Resources

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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 #6 : How To Find The Volume Of A Pyramid

Example Question #7 : How To Find The Volume Of A Pyramid

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

Example Question #8 : How To Find The Volume Of A Pyramid

Example Question #3 : How To Find The Volume Of A Pyramid

Example Question #721 : Geometry

Example Question #722 : Geometry

Example Question #111 : Volume Of A Three Dimensional Figure

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

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

All SSAT Upper Level Math Resources

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