Question

The depth of water in a tank that’s in the shape of a rectangular prism is inversely proportional to the area of its base if the tank’s volume is kept constant. If the area of the tank’s base is 200 square feet, the depth of the water in the tank is 12 feet. Which pair of statements best describe this situation?
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.
B.
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 6 feet.
C.
If the depth is 8 feet, the area of the base is 240 square feet. And if the area of the base is 600 square feet, the depth of the water is 4 feet.
D.
If the depth is 8 feet, the area of the base is 240 square feet. And if the area of the base is 600 square feet, the depth of the water is 6 feet.

Answer 1

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 2

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,

$A\propto \frac{1}{h}$

$A= \frac{k}{h}$

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,

$200= \frac{k}{12}$

$\frac{1}{200}= \frac{12}{k}$

$k= 2400$

Therefore, the relation between area of the base and height of the prism is,

$A= \frac{2400}{h}$

When h = 8 feet,

$A= \frac{2400}{8}=300\text{ square feet}$

Also, when A = 600 square feet,

$600= \frac{2400}{h}$

$h= \frac{2400}{600}=4\text{ feet}$

Therefore, Option A is correct.