Question

***HELP****HELP***
The area of the base of a rectangular prism is 24 square inches, and its height is a whole number. Which of the following could not be its volume?

120 in3
144 in3
160 in3
168 in3

Answer 1

You know the volume of a prism is lwh. The base is given. Which is lw.
Set lw = 24.

plug this back into the original equation
lwh = v
24h = v

now substitute in the given volumes and isolate the height fro each set.

h = 120/24 = 5
h = 144/24 = 6
h = 160/24 = 6.66666
h = 168/24 = 7

The question states the height is a whole number which eliminates the third option as a possible height.

Answer 2

V = base * height
-> h = v/base
Since h is whole number -> V is divisable to base
=> Only V = 160 is undivisable to 24!