An aboveground pool is 5ft tall with a diameter of 40 ft is filled with water in 50 minutes. How long will it take to fill an aboveground pool that is 6ft tall with a diameter of 36 ft?
What did you not understand about my previous response?
To determine how long it will take to fill the larger aboveground pool, we need to understand the relationship between the volume of the pool and the time it takes to fill it.
The volume of a cylindrical pool can be calculated using the formula V = π * r^2 * h, where V is the volume, π is a constant approximately equal to 3.14159, r is the radius of the pool, and h is the height of the pool.
Let's calculate the volume of the original pool with a height of 5 ft and diameter of 40 ft. To find the radius (r), we divide the diameter by 2: r = 40 ft / 2 = 20 ft.
Now we can calculate the volume:
V = π * r^2 * h
V = 3.14159 * (20 ft)^2 * 5 ft
V ≈ 3.14159 * 400 sq. ft * 5 ft
V ≈ 6283 sq. ft * 5 ft
V ≈ 31,415 cubic ft
Next, we need to determine the rate of filling the original pool. We know that it takes 50 minutes to fill the pool, so we can calculate the filling rate as volume per minute:
Rate = 31,415 cubic ft / 50 minutes
Rate ≈ 628.3 cubic ft/minute
Now, let's calculate how long it would take to fill the larger pool, which has a height of 6 ft and a diameter of 36 ft. First, we calculate the volume of this pool using the same formula.
The radius (r) is calculated as diameter divided by 2: r = 36 ft / 2 = 18 ft.
Volume:
V = π * r^2 * h
V = 3.14159 * (18 ft)^2 * 6 ft
V ≈ 3.14159 * 324 sq. ft * 6 ft
V ≈ 6082.1236 cubic ft
Now, we need to calculate the time it will take to fill this pool at the given filling rate:
Time = V / Rate
Time ≈ 6082.1236 cubic ft / 628.3 cubic ft/minute
Time ≈ 9.69 minutes
Therefore, it will take approximately 9.69 minutes to fill an aboveground pool that is 6 ft tall with a diameter of 36 ft.