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
Plug in the values, starting with the first equation.
D = 2r, therefore D/2 = r
Put the value of r in the second equation to find A.
Put the value of A in the third equation to find V.
W = # of gallons = 7.5V
You can do the calculations.
To find the number of gallons needed to fill the swimming pool, we can follow these steps:
Step 1: Find the radius of the swimming pool.
Given that the diameter is 15 feet, we can find the radius (r) by dividing the diameter by 2.
r = 15/2 = 7.5 feet.
Step 2: Find the area (A) of the swimming pool.
Using the formula A = πr^2, we can calculate the area.
A = π * (7.5)^2 = 176.71 square feet.
Step 3: Find the volume (V) of the swimming pool.
Since the pool is 4 feet deep, the volume can be found using the formula V = 4A.
V = 4 * 176.71 = 706.84 cubic feet.
Step 4: Calculate the number of gallons needed.
Using the conversion factor given that it takes 7.5 gallons to fill one cubic foot, we can calculate the number of gallons needed.
W = 7.5 * V = 7.5 * 706.84 = 5,301.3 gallons.
Therefore, to the nearest whole number, approximately 5,301 gallons are needed to fill the swimming pool.
To find the number of gallons needed to fill the swimming pool, we need to calculate the volume of the pool and then multiply it by the conversion factor of 7.5 gallons per cubic foot.
First, let's find the radius of the circular swimming pool. The diameter of the pool is given as 15 feet, and we know that the diameter is twice the radius. So, the radius (r) would be half of the diameter.
r = 15 / 2 = 7.5 feet
Now, let's calculate the area of the circular swimming pool. The formula for the area of a circle is A = π * r^2.
A = π * (7.5)^2
A ≈ 176.71 square feet
Next, we need to calculate the volume of the swimming pool. The formula for the volume of a cylinder (like a circular swimming pool) is V = height * area of the base.
In this case, the height of the pool is given as 4 feet.
V = 4 * 176.71
V ≈ 706.84 cubic feet
Finally, we can calculate the number of gallons needed to fill the swimming pool by multiplying the volume by the conversion factor of 7.5 gallons per cubic foot.
W = 7.5 * 706.84
W ≈ 5301.3 gallons
To the nearest whole number, approximately 5301 gallons are needed to fill this swimming pool.