the volume of a rectangular prism is 144 cubic inches. The height of the prism is 8 inches. Which measurments, in inches, could be the dimensions of the base?
If the volume V = 144 cubic inches, and V = length*width*height,
then 144 cubic inches = length*width*8 inches
and length*width = 144/8 square inches = 18 square inches.
This means that the length and width can be any pair of numbers that has a product of 18.
Examples: 2*9, 1*18, 1/2*36, etc.
Keep in mind that the dimensions aren't necessarily whole numbers! There are actually infinitely many answers to this problem, so think of a way to describe the solution set in general terms.
You divide 144 cubic inches by 8 inches (height) because you must use inverse operations on both sides of the equation to isolate the length x width. The inverse operation of multiplication is division, so the following is the application of division to the problem, broken down:
`144=l times w times 8`
`144 div 8=l times w times 8 div 8`
`18=l times w`
Volume of a rectangular prism V=length*width*height
In other words the volume of a prism is the product of the area of the base and the height.
Given Volume = 144 cubic inches
height = 8 inches
Plugging these values in the above formula we get:
area of the base = 144/8 = 18 square inches.
Therefore, the dimensions of the base can be any pair of whole numbers or decimal numbers whose product is 18. There will be many solutions.
Hence, the possible dimensions are 9in by 2in or 2.5in by 7.2in etc.