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?
time is proprotional to volume. Volume=constant*height*radisu^2
time=50min(6/4)(18/20)^2=
To determine how long it will take to fill the aboveground pool, we can use the concept of ratios.
First, let's calculate the volume of the first pool with a diameter of 40ft and a height of 5ft. The formula to calculate the volume of a cylinder is: V = πr²h, where V is the volume, π is Pi (approximately 3.14), r is the radius, and h is the height.
The radius of the first pool is half the diameter, so the radius is 40ft / 2 = 20ft. Plugging these values into the formula, we have:
V1 = π(20ft)²(5ft)
≈ 3.14 * 400ft² * 5ft
≈ 6280ft³
Now, we need to find out the rate at which the water is being poured into the pool. From the information provided, we know that the first pool is filled in 50 minutes.
So, the rate of filling the first pool is: 6280ft³ / 50 minutes = 125.6 ft³/minute (rounded to one decimal place).
Next, let's find out how long it will take to fill the second pool, which has a diameter of 36ft and a height of 6ft. We'll use the same formula to calculate the volume of the second pool.
The radius of the second pool is half the diameter, so the radius is 36ft / 2 = 18ft. Plugging these values into the formula, we have:
V2 = π(18ft)²(6ft)
≈ 3.14 * 324ft² * 6ft
≈ 6085ft³
Now, we can use the rate we calculated earlier to determine the time it will take to fill the second pool. We'll rearrange the equation to isolate the time:
Time = Volume / Rate
Time = 6085ft³ / 125.6 ft³/minute
Using a calculator, we can calculate this as:
Time ≈ 48.5 minutes
Therefore, it will take approximately 48.5 minutes to fill the aboveground pool that is 6ft tall with a diameter of 36ft.