The area of the base of a tank is 100 sq. ft. It takes 20 second to fill the tank with water poured at rate of 25 cubic feet per second. What is the height in feet of the rectangluar tank?

Options

A. 0.25
B. 0.5
C. 1
D. 5

Answer

To find the height of the rectangular tank, we can follow these steps:

### Step 1: Understand the given information
We know the following:
- The area of the base of the tank (A) = 100 square feet
- The rate at which water is poured into the tank = 25 cubic feet per second
- The time taken to fill the tank = 20 seconds

### Step 2: Calculate the total volume of water poured into the tank
The total volume (V) of water poured into the tank can be calculated using the formula:
\[ V = \text{Rate} \times \text{Time} \]
Substituting the given values:
\[ V = 25 \, \text{cubic feet/second} \times 20 \, \text{seconds} = 500 \, \text{cubic feet} \]

### Step 3: Relate volume to height
The volume of a rectangular tank can also be expressed as:
\[ V = \text{Area of base} \times \text{Height} \]
Let the height of the tank be \( h \) feet. Therefore:
\[ V = 100 \, \text{square feet} \times h \]

### Step 4: Set the two volume expressions equal to each other
Since both expressions represent the volume of the tank, we can set them equal:
\[ 100h = 500 \]

### Step 5: Solve for height \( h \)
To find \( h \), divide both sides by 100:
\[ h = \frac{500}{100} = 5 \, \text{feet} \]

### Conclusion
The height of the rectangular tank is 5 feet.

---