# SAT II Math I : Other 3-Dimensional Geometry

## Example Questions

### Example Question #1 : Other 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:

Explanation:

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:

Explanation:

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:

Explanation:

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