Question
A cylindrical pool has a diameter of 22 feet and can be filled to a height of 4 feet. The pool already has 600 cubic feet of water in it. A hose is filling the pool at a rate of 2 cubic feet per minute.
Question
To the nearest minute, how much longer will it take to fill the pool? Enter the answer in the box.
Question
To the nearest minute, how much longer will it take to fill the pool? Enter the answer in the box.
Answers
GPT-4o mini
To determine how much longer it will take to fill the cylindrical pool, we first need to calculate the total volume of the pool and then find out how much more water is needed.
1. **Calculate the radius of the pool**:
The diameter of the pool is 22 feet, so the radius \( r \) is half of that:
\[
r = \frac{22}{2} = 11 \text{ feet}
\]
2. **Calculate the total volume of the pool**:
The formula for the volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where \( h \) is the height of the pool. In this case, the height \( h \) is 4 feet.
\[
V = \pi (11^2)(4) = \pi (121)(4) = 484\pi
\]
Using the approximate value of \( \pi \approx 3.14 \):
\[
V \approx 484 \times 3.14 \approx 1520.56 \text{ cubic feet}
\]
3. **Determine how much volume is already in the pool**:
The pool currently has 600 cubic feet of water.
4. **Calculate the remaining volume needed to fill the pool**:
\[
\text{Remaining Volume} = \text{Total Volume} - \text{Current Volume} = 1520.56 - 600 = 920.56 \text{ cubic feet}
\]
5. **Determine the rate at which the pool is being filled**:
The hose fills the pool at a rate of 2 cubic feet per minute.
6. **Calculate how long it will take to fill the remaining volume**:
\[
\text{Time} = \frac{\text{Remaining Volume}}{\text{Rate}} = \frac{920.56}{2} \approx 460.28 \text{ minutes}
\]
To find the answer to the nearest minute:
\[
\text{Time} \approx 460 \text{ minutes}
\]
Thus, it will take approximately **460 minutes** to fill the pool.
1. **Calculate the radius of the pool**:
The diameter of the pool is 22 feet, so the radius \( r \) is half of that:
\[
r = \frac{22}{2} = 11 \text{ feet}
\]
2. **Calculate the total volume of the pool**:
The formula for the volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where \( h \) is the height of the pool. In this case, the height \( h \) is 4 feet.
\[
V = \pi (11^2)(4) = \pi (121)(4) = 484\pi
\]
Using the approximate value of \( \pi \approx 3.14 \):
\[
V \approx 484 \times 3.14 \approx 1520.56 \text{ cubic feet}
\]
3. **Determine how much volume is already in the pool**:
The pool currently has 600 cubic feet of water.
4. **Calculate the remaining volume needed to fill the pool**:
\[
\text{Remaining Volume} = \text{Total Volume} - \text{Current Volume} = 1520.56 - 600 = 920.56 \text{ cubic feet}
\]
5. **Determine the rate at which the pool is being filled**:
The hose fills the pool at a rate of 2 cubic feet per minute.
6. **Calculate how long it will take to fill the remaining volume**:
\[
\text{Time} = \frac{\text{Remaining Volume}}{\text{Rate}} = \frac{920.56}{2} \approx 460.28 \text{ minutes}
\]
To find the answer to the nearest minute:
\[
\text{Time} \approx 460 \text{ minutes}
\]
Thus, it will take approximately **460 minutes** to fill the pool.