Answer:
A.
If the depth is 8 feet, the area of the base is 300 square feet. And if the area of the base is 600 square feet, the depth of the water is 4 feet.
Step-by-step explanation:
Depth = Volume/Area
d = V/A
12 = V/200
V = 12 × 200
= 2,400
When d = 8, A = 300
V = dA
= 8 × 300
= 2,400
When d = 4, A = 600
V = 4 × 600
= 2,400.
The first option is correct.
Answer: A. If the depth is 8 feet, the area of the base is 300 square feet. And if the area of the base is 600 square feet, the depth of the water is 4 feet.
Step-by-step explanation:
Let A represents the area of the base of given rectangular prism and h be the height of the prism.
Then, According to the question,
[tex]A\propto \frac{1}{h}[/tex]
[tex]A= \frac{k}{h}[/tex]
Where k is the proportional constant,
Since, If the area of the tank’s base is 200 square feet, the depth of the water in the tank is 12 feet.
By putting A = 200 and h = 12 in the above relation,
We get,
[tex]200= \frac{k}{12}[/tex]
[tex]\frac{1}{200}= \frac{12}{k}[/tex]
[tex]k= 2400[/tex]
Therefore, the relation between area of the base and height of the prism is,
[tex]A= \frac{2400}{h}[/tex]
When h = 8 feet,
[tex]A= \frac{2400}{8}=300\text{ square feet}[/tex]
Also, when A = 600 square feet,
[tex]600= \frac{2400}{h}[/tex]
[tex]h= \frac{2400}{600}=4\text{ feet}[/tex]
Therefore, Option A is correct.
