### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Tetrahedrons

A triangular pyramid, or tetrahedron, with volume 100 has four vertices with Cartesian coordinates

where .

Evaluate .

**Possible Answers:**

**Correct answer:**

The tetrahedron is as follows (figure not to scale):

This is a triangular pyramid with a right triangle with legs 10 and as its base; the area of the base is

The height of the pyramid is 5, so

Set this equal to 100 to get :

### Example Question #2 : Tetrahedrons

A triangular pyramid, or tetrahedron, with volume 1,000 has four vertices with Cartesian coordinates

where .

Evaluate .

**Possible Answers:**

**Correct answer:**

The tetrahedron is as follows:

This is a triangular pyramid with a right triangle with two legs of measure as its base; the area of the base is

Since the height of the pyramid is also , the volume is

.

Set this equal to 1,000:

### Example Question #3 : Tetrahedrons

A triangular pyramid, or tetrahedron, with volume 240 has four vertices with Cartesian coordinates

where .

Evaluate .

**Possible Answers:**

**Correct answer:**

The tetrahedron is as follows (figure not to scale):

This is a triangular pyramid with a right triangle with two legs of measure as its base; the area of the base is

The height of the pyramid is 24, so the volume is

Set this equal to 240 to get :