70 POINTS PLEASE HELP! A dump truck pours sand into a container in the shape of a rectangular prism with a square base of length

Question

2 years ago

6

2 feet. SEE PICTURE FOR REST

2 answers:

galina1969 [7] · Answer 1 · 2022-03-04T16:46:59+03:00

Answer:

A

Step-by-step explanation:

The volume of a rectangular prism is:

$V=\ell wh$

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:

$V=(2)(2)h=4h$

So, we can write:

$V=4h$

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:

$\displaystyle V=4\Big(\frac{2}{3}\Big)t=\frac{8}{3}t$

We want to find after how long it will be until the volume is 64 cubic feet. So, V = 64:

$\displaystyle 64 = \frac{8}{3} t$

Solve for t:

$\displaystyle t=\frac{3}{8}(64)=3(8)=24\text{ minutes}$

The correct answer is A.

masha68 [24] · Answer 2 · 2022-03-04T19:10:44+03:00

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