### All SAT II Math I Resources

## Example Questions

### Example Question #56 : 3 Dimensional Geometry

A rectangular prism has a height of 4 in., length of 8in., and a width of 7in. Find the volume of the prism.

**Possible Answers:**

**Correct answer:**

To find the volume of a rectangular prism we use the equation of:

Now substituting in our values we get:

### Example Question #1 : Other 3 Dimensional Geometry

What is the volume of a triangular prism having a base of 2, a height of 8, and second height of 14?

**Possible Answers:**

**Correct answer:**

To find the volume of a triangular prism we use the equation

In our case our

Therefore,

### Example Question #1 : Other 3 Dimensional Geometry

If a cube has a surface area of then what is the the length of its longest diagonal?

**Possible Answers:**

**Correct answer:**

The longest diagonal of a cube transverses the interior of the figure:

This distance is defined by the super pythagorean theorem :

where , , and are the length, width, and height. Because the figure is a cube, all three are the same measure, and each is the side of the cube.

We can use the given surface area to find the length of the side:

We can use this value for the side to plug into the super pythagorean theorem

Which can be simplified to

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