Advanced Geometry : Tetrahedrons

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

Example Question #5 : 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 #6 : 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 and substitute in the provided edge length.

Rationalize the denominator to arrive at the correct answer.

 

Example Question #7 : How To Find The Volume Of A Tetrahedron

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 #8 : How To Find The Volume Of A Tetrahedron

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 #9 : 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 #10 : 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."

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

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 doubled.

It is 8 times greater.

It cannot be determined by the information given.

It increases by 50%.

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 : 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 ,

 

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

Example Question #13 : How To Find The Volume Of A Tetrahedron

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 : How To Find The Volume Of A Tetrahedron

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.

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