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SSAT Upper Level Math : How to find the volume of a tetrahedron

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #41 : Volume Of A Three Dimensional Figure

Find the volume of a tetrahedron with side lengths of .

Possible Answers:

$168\sqrt2$

$1728\sqrt2$

$966\sqrt2$

$144\sqrt2$

Correct answer:

$144\sqrt2$

Explanation:

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}12^3$

$\text{Volume}=\frac{1728\sqrt2}{12}$

$\text{Volume}=144\sqrt2$

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Example Question #12 : How To Find The Volume Of A Tetrahedron

Find the volume of a regular tetrahedron with side lengths of .

Possible Answers:

$\frac{250\sqrt2}{3}$

$125\sqrt2$

$\frac{500\sqrt2}{3}$

$\frac{1000\sqrt2}{3}$

Correct answer:

$\frac{250\sqrt2}{3}$

Explanation:

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}10^3$

$\text{Volume}=\frac{1000\sqrt2}{12}$

$\text{Volume}=\frac{250\sqrt2}{3}$

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Example Question #51 : Volume Of A Three Dimensional Figure

Find the volume of a regular tetrahedron with side lengths of .

Possible Answers:

$\frac{4x^3\sqrt2}{3}$

$8x^3\sqrt2$

$\frac{3x^3\sqrt2}{4}$

$\frac{2x^3\sqrt2}{3}$

Correct answer:

$\frac{2x^3\sqrt2}{3}$

Explanation:

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}(2x)^3$

$\text{Volume}=\frac{8x^3\sqrt2}{12}$

$\text{Volume}=\frac{2x^3\sqrt2}{3}$

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Example Question #51 : Volume Of A Three Dimensional Figure

Find the volume of a regular tetrahedron with side lengths of .

Possible Answers:

$16a^3\sqrt2$

$\frac{32a^3\sqrt2}{3}$

$64a^3\sqrt2$

$\frac{16a^3\sqrt2}{3}$

Correct answer:

$\frac{16a^3\sqrt2}{3}$

Explanation:

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}(4a)^3$

$\text{Volume}=\frac{64a^3\sqrt2}{12}$

$\text{Volume}=\frac{16a^3\sqrt2}{3}$

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Example Question #51 : Volume Of A Three Dimensional Figure

Find the volume of a regular tetrahedron with side lengths of 12h .

Possible Answers:

$1796h^3\sqrt2$

$144h^3\sqrt2$

$288h^3\sqrt2$

$966h^3\sqrt2$

Correct answer:

$144h^3\sqrt2$

Explanation:

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}(12h)^3$

$\text{Volume}=\frac{1728h^3\sqrt2}{12}$

$\text{Volume}=144h^3\sqrt2$

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Example Question #16 : How To Find The Volume Of A Tetrahedron

Find the volume of a regular tetrahedron with side lengths of $\frac{1}{2}$ .

Possible Answers:

$\frac{\sqrt2}{48}$

$\frac{\sqrt2}{96}$

$\frac{4\sqrt2}{3}$

$\frac{\sqrt2}{24}$

Correct answer:

$\frac{\sqrt2}{96}$

Explanation:

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}(\frac{1}{2})^3$

$\text{Volume}=\frac{\sqrt2}{12}(\frac{1}{8})$

$\text{Volume}=\frac{\sqrt2}{96}$

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Example Question #11 : How To Find The Volume Of A Tetrahedron

Find the volume of a regular tetrahedron with side lengths of $\frac{1}{3}$ .

Possible Answers:

$\frac{\sqrt2}{27}$

$\frac{\sqrt2}{12}$

$\frac{\sqrt2}{324}$

$\frac{\sqrt2}{54}$

Correct answer:

$\frac{\sqrt2}{324}$

Explanation:

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}(\frac{1}{3})^3$

$\text{Volume}=\frac{\sqrt2}{12}(\frac{1}{27})$

$\text{Volume}=\frac{\sqrt2}{324}$

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SSAT Upper Level Math : How to find the volume of a tetrahedron

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #41 : Volume Of A Three Dimensional Figure

Example Question #12 : How To Find The Volume Of A Tetrahedron

Example Question #51 : Volume Of A Three Dimensional Figure

Example Question #51 : Volume Of A Three Dimensional Figure

Example Question #51 : Volume Of A Three Dimensional Figure

Example Question #16 : How To Find The Volume Of A Tetrahedron

Example Question #11 : How To Find The Volume Of A Tetrahedron

All SSAT Upper Level Math Resources

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