PSAT Math : How to find the volume of a tetrahedron

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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

Tetra_2

Note: Figure NOT drawn to scale.

The above triangular pyramid has volume 25. To the nearest tenth, evaluate .

Possible Answers:

Insufficient information is given to answer the problem.

Correct answer:

Explanation:

We are looking for the height of the pyramid.

The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

The height  of a pyramid can be calculated using the fomula

We set  and  and solve for :

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

Tetra_1

Note: Figure NOT drawn to scale.

Give the volume (nearest tenth) of the above triangular pyramid.

Possible Answers:

Correct answer:

Explanation:

The height of the pyramid is . The base is an equilateral triangle with sidelength 4, so its area can be calculated as follows:

The volume of a pyramid can be calculated using the fomula

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

A regular tetrahedron has an edge length of . What is its volume?

Possible Answers:

Correct answer:

Explanation:

The volume of a tetrahedron is found with the equation , where  represents the length of an edge of the tetrahedron.

Plug in 4 for the edge length and reduce as much as possible to find the answer:

 

The volume of the tetrahedron is .

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