A circular swimming pool is 4 feet deep and has a diameter of 15 feet. If it takes 7.5 gallons of water to fill one cubic foot, to the nearest whole number, how many gallons are needed to fill this swimming pool.
Diameter = 2r
A = π r^2
V = 4A
W = 7.5V
You can do the calculations.
Can someone do the calculations?
To find the number of gallons needed to fill the swimming pool, we need to calculate the volume of the pool and then convert it to gallons.
The volume of a cylinder (which can approximate the shape of a swimming pool) can be found using the formula:
V = π * r² * h
where:
V = volume of the cylinder
π = pi (approximately 3.14159...)
r = radius of the cylinder (which is half the diameter)
h = height (depth) of the cylinder
Given that the diameter of the swimming pool is 15 feet, the radius can be calculated as follows:
r = diameter / 2 = 15 feet / 2 = 7.5 feet
The depth (height) of the swimming pool is given as 4 feet.
To calculate the volume of the swimming pool, substitute the values into the formula:
V = π * (7.5 ft)² * 4 ft
Now, let's calculate the volume:
V = 3.14159 * 7.5² * 4
V ≈ 3.14159 * 56.25 * 4
V ≈ 706.857196875
The volume of the swimming pool is approximately 706.857 cubic feet.
To convert this volume from cubic feet to gallons, we use the conversion rate of 7.5 gallons per cubic foot. Multiply the volume by the conversion rate:
Gallons = Volume * Conversion rate
Gallons ≈ 706.857 * 7.5
Gallons ≈ 5301.428125
Therefore, approximately 5301 gallons are needed to fill this swimming pool.