How many cubes with a side length of 4 inches will fit into a rectangular box with the dimensions 12 x 24 x 32?
Note: In the math section of the SAT, you will encounter questions that do not have answer choices. Instead of bubbling in a letter, you will bubble in your answer. These questions are called grid in questions, and you should always guess an answer for them because there is no penalty for getting the question wrong!
Read the question carefully. You need to glean every relevant fact from this question, such as the fact that you are dealing with two different solids: a cube and a rectangular prism.
Identify the bottom line. You want the number of cubes that fit in the rectangular prism.
Assess your options. You could try to draw out the scenario, but there is no need to do this. Instead, notice that you are dividing space in a box to see how many cubes will fit. You can divide all of the dimensions of the box by all of the dimensions of the cube.
Attack the problem. You know how big the box is: 12 x 24 x 32. You also know that a cube has the same length for each side. The cube's dimensions are 4 x 4 x 4.
In order to find out how many cubes fit in the box, you can simply divide the space of the box by the space of the cube:
4 x 4 x 4
The answer to this problem will be your solution. However, before you start plugging this into your calculator, notice that each dimension is divisible by 4. You can simplify the fraction by dividing each of the prism's dimensions by the cube's dimensions. You are essentially canceling out 4s from the fraction. Your problem is now:
3 x 6 x 8
This method will save you a lot of time that you can spend on harder problems! Now simply solve the problem.
3 x 6 x 8 = 144
Loop back. You divided the whole space by the amount of space taken up by a single cube, so you know that 144 cubes will fit in this box.
The correct answer is 144.
This is a medium level question.