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 #11 : Volume

How is the volume of a regular tetrahedron effected when the length of each edge is doubled?

Possible Answers:

It is 4 times greater.

It is 8 times greater.

It increases by 50%.

It is doubled.

It cannot be determined by the information given.

Correct answer:

It is 8 times greater.

Explanation:

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

The volume of the same tetrahedron when the length of the edges are doubled would be .

Therefore,

 

Example Question #12 : Volume

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 ,

 

And, of course, volume should be in cubic measurements!

Example Question #13 : Volume

Find the volume of a regular tetrahedron if one of its edges is  long.

Possible Answers:

Correct answer:

Explanation:

Write the volume equation for a tetrahedron.

In this formula,  stands for the tetrahedron's volume and  stands for the length of one of its edges.

Substitute the given edge length and solve.

Rationalize the denominator.

Example Question #14 : Volume

Find the volume of a tetrahedron if the side length is .

Possible Answers:

Correct answer:

Explanation:

Write the equation to find the volume of a tetrahedron.

Substitute the side length and solve for the volume.

Rationalize the denominator.

Example Question #21 : 3 Dimensional Geometry

What is the volume of a regular tetrahedron with an edge length of 6?

Possible Answers:

Correct answer:

Explanation:

The volume of a tetrahedron can be solved for by using the equation:

where  is the measurement of the edge of the tetrahedron. 

This problem can be quickly solved by substituting 6 in for

Example Question #22 : 3 Dimensional Geometry

What is the volume of the tetrahedron shown below? 


Screen shot 2015 10 21 at 7.16.10 pm

Possible Answers:

Correct answer:

Explanation:

The volume of a tetrahedron is .

This tetrahedron has a side with a length of 8. 

, which becomes .

You can reduce that answer further, so that it becomes 

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