Question

A cylindrical water tank has a radius of 2 12 feet and a height of 6 feet. If water flows into the tank at a rate of 5
6
cubic foot per minute, how long will it take to fill the tank? (Use π ≈ 3.14 and round your answer to the nearest
minute.) Show your work

Answer 1

To find out how long it will take to fill the cylindrical water tank, we first need to calculate the volume of the tank and then use the rate at which water flows into it.

### Step 1: Calculate the Volume of the Cylindrical Tank

The formula for the volume \( V \) of a cylinder is given by:

\[
V = \pi r^2 h
\]

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.

#### Given:
- Radius \( r = 2 \frac{1}{2} \) feet = \( 2.5 \) feet
- Height \( h = 6 \) feet

#### Substituting the values:

\[
V = 3.14 \times (2.5)^2 \times 6
\]

Calculating \( (2.5)^2 \):

\[
(2.5)^2 = 6.25
\]

Now substituting back into the volume formula:

\[
V = 3.14 \times 6.25 \times 6
\]

Calculating \( 6.25 \times 6 \):

\[
6.25 \times 6 = 37.5
\]

Now substituting this value into the equation for volume:

\[
V = 3.14 \times 37.5
\]

Calculating \( 3.14 \times 37.5 \):

\[
V \approx 117.75 \text{ cubic feet}
\]

### Step 2: Determine the Time to Fill the Tank

Water is flowing into the tank at a rate of \( 5 \frac{6}{\text{cubic foot per minute}} \). First, we need to convert \( 5 \frac{6}{\text{cubic foot per minute}} \) into a decimal:

\[
5 \frac{6}{\text{cubic foot}} = 5.6 \text{ cubic foot per minute}
\]

Now, to find the time \( t \) it takes to fill the tank, we use the formula:

\[
t = \frac{V}{\text{rate}}
\]

Substituting the values we have:

\[
t = \frac{117.75}{5.6}
\]

Calculating this gives:

\[
t \approx 20.94 \text{ minutes}
\]

### Step 3: Round to the Nearest Minute
Rounding \( 20.94 \) to the nearest minute:

\[
t \approx 21 \text{ minutes}
\]

### Final Answer
It will take approximately **21 minutes** to fill the cylindrical water tank.