All SAT II Math I Resources
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.
To find the volume of a rectangular prism we use the equation of:
Now substituting in our values we get:
Example Question #2 : 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?
To find the volume of a triangular prism we use the equation
In our case our
Example Question #3 : Other 3 Dimensional Geometry
If a cube has a surface area of then what is the the length of its longest diagonal?
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