Answer:
A
Step-by-step explanation:
The volume of a rectangular prism is:
[tex]V=\ell wh[/tex]
Since the prism has a square base, each side length being 2, this means that both the length and width of our prism is 2. Therefore:
[tex]V=(2)(2)h=4h[/tex]
So, we can write:
[tex]V=4h[/tex]
The height h increases at a rate of about 8 inches or 8/12 = 2/3 feet per minute.
So, after t minutes, the height will be 2/3(t) feet. Thus, we can substitute:
[tex]\displaystyle V=4\Big(\frac{2}{3}\Big)t=\frac{8}{3}t[/tex]
We want to find after how long it will be until the volume is 64 cubic feet. So, V = 64:
[tex]\displaystyle 64 = \frac{8}{3} t[/tex]
Solve for t:
[tex]\displaystyle t=\frac{3}{8}(64)=3(8)=24\text{ minutes}[/tex]
The correct answer is A.
