Advanced Geometry : How to find the volume of a tetrahedron

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

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

What is the volume of the following tetrahedron? Assume the figure is a regular tetrahedron.

Tetrahedron

Possible Answers:

Correct answer:

Explanation:

A regular tetrahedron is composed of four equilateral triangles. The formula for the volume of a regular tetrahedron is:

, where  represents the length of the side.

Plugging in our values we get:

Example Question #8 : 3 Dimensional Geometry

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a tetrahedron.

Substitute in the length of the edge provided in the problem.

Rationalize the denominator.

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

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a tetrahedron.

Substitute in the length of the edge provided in the problem:

Cancel out the  in the denominator with one in the numerator:

A square root is being raised to the power of two in the numerator; these two operations cancel each other out. After canceling those operations, reduce the remaining fraction to arrive at the correct answer:

Example Question #10 : 3 Dimensional Geometry

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for finding the volume of a tetrahedron.

Substitute in the edge length provided in the problem. 

Cancel out the  in the denominator with part of the  in the numerator:

Expand, rationalize the denominator, and reduce to arrive at the correct answer:

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

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula the volume of a tetrahedron.

Substitute the edge length provided in the equation into the formula.

Cancel out the denominator with part of the numerator and solve the remaining part of the numerator to arrive at the correct answer.

Example Question #42 : Tetrahedrons

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula the volume of a tetrahedron and substitute in the provided edge length.

Rationalize the denominator to arrive at the correct answer.

 

Example Question #81 : Advanced Geometry

Find the volume of the regular tetrahedron with side length .

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a regular tetrahedron is:

Where  is the length of side. Using this formula and the given values, we get:

Example Question #82 : Advanced Geometry

What is the volume of a regular tetrahedron with edges of ?

Possible Answers:

Correct answer:

Explanation:

The volume of a tetrahedron is found with the formula:

  ,

where  is the length of the edges.

When 

.

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

What is the volume of a regular tetrahedron with edges of ?

Possible Answers:

None of the above.

Correct answer:

Explanation:

The volume of a tetrahedron is found with the formula,

  where  is the length of the edges.

When  the volume becomes,

The answer is in volume, so it must be in a cubic measurement!

Example Question #5 : How To Find The Volume Of A Tetrahedron

What is the volume of a regular tetrahedron with edges of ?

Possible Answers:

None of the above.

 

 

Correct answer:

None of the above.

Explanation:

The volume of a tetrahedron is found with the formula  where  is the length of the edges.

When 

 

This answer is not found, so it is "none of the above."

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