### All Advanced Geometry Resources

## Example Questions

### 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.

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:**

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:**

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:**

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:**

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?

**Possible Answers:**

**Correct answer:**

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

.

Certified Tutor