Advanced Geometry : How to find the volume of a tetrahedron

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.

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 #1 : How To Find The Volume Of A Tetrahedron

Find the volume of a tetrahedron with an edge of .

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 #1 : How To Find The Volume Of A Tetrahedron

Find the volume of a tetrahedron with an edge of .

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 #1 : How To Find The Volume Of A Tetrahedron

Find the volume of a tetrahedron with an edge of .

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 #1 : How To Find The Volume Of A Tetrahedron

Find the volume of a tetrahedron with an edge of .

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 #1 : How To Find The Volume Of A Tetrahedron

Find the volume of a tetrahedron with an edge of .

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 #1 : How To Find The Volume Of A Tetrahedron

Find the volume of the regular tetrahedron with side length .

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 #1 : How To Find The Volume Of A Tetrahedron

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

Explanation:

The volume of a tetrahedron is found with the formula:

,

where  is the length of the edges.

When

.

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

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

None of the above.

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 #1 : How To Find The Volume Of A Tetrahedron

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

None of the above.

None of the above.

Explanation:

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

When