### All PSAT Math Resources

## Example Questions

### Example Question #80 : Solid Geometry

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:**

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 #1 : How To Find The Volume Of A Tetrahedron

Note: Figure NOT drawn to scale.

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

**Possible Answers:**

**Correct answer:**

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 #2 : Tetrahedrons

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

**Possible Answers:**

**Correct answer:**

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 .