Final answer:
To determine the cost to fill a circular pool with a 20-foot diameter and a 5-foot depth, first calculate the pool's volume, convert the volume into gallons, and then multiply the gallons by the water cost per gallon. The cost to fill the pool is approximately $35 to the nearest dollar.
Step-by-step explanation:
Cost to Fill a Circular Pool
To determine the cost to fill a circular pool that has a diameter of 20 feet and a depth of 5 feet, we first need to calculate the volume of the pool. The volume V of a cylinder (which is the shape of the pool) can be found using the formula V = πr^2h, where r is the radius and h is the depth of the cylinder. In this case, the radius is half the diameter, so r = 10 feet, and h = 5 feet.
Calculating the Volume:
- Radius (r) = 10 feet (half of the diameter)
- Depth (h) = 5 feet
- Volume (V) = π * (10)^2 * 5 = 1,570 feet^3 (rounded to the nearest cubic foot)
Next, we convert the volume in cubic feet to gallons. Since one cubic foot contains approximately 7.48 gallons, we multiply the volume by this amount:
Total gallons = 1,570 * 7.48 = 11,743.6 gallons (rounded to the nearest gallon)
Finally, we calculate the cost to fill the pool with water. Water costs $3 per thousand gallons. So the total cost will be the number of thousand gallons multiplied by $3:
Calculating the Cost:
- Total gallons = 11,744 (rounded up to the nearest gallon)
- Thousands of gallons = 11,744 / 1,000 ≈ 11.744
- Cost = 11.744 * $3 ≈ $35.23
The cost to fill the pool, to the nearest dollar, will be $35.