Question

A circular backyard pool has a diameter of 26 feet and is 4 feet deep. One cubic foot of water has a capacity of approximately 7.48 gallons. If water costs $2 per thousand gallons, how much, to the nearest dollar, will it cost to fill the pool?

Answer 1

To fill the circular pool, we need to find its volume and convert it to gallons. The volume of the pool is calculated using the formula for the volume of a cylinder. The cost is then determined by multiplying the number of gallons by the cost per thousand gallons.

Step-by-step explanation:

To calculate the cost of filling the circular pool, we need to find the volume of the pool and then convert it to gallons. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

In this case, the diameter is given as 26 feet, so the radius is half of that, which is 13 feet. The height is given as 4 feet. Substituting these values into the formula, we get V = π(13^2)(4) = 676π cubic feet.

To convert cubic feet to gallons, we multiply by the conversion factor of 7.48 gallons/cubic foot. So, the total number of gallons needed to fill the pool is (676π)(7.48) = approximately 15,939 gallons.

Finally, to find the cost, we divide the number of gallons by a thousand and multiply by the cost per thousand gallons. In this case, we have (15,939/1000) * 2 = approximately $31.88. Therefore, it will cost approximately $32 to fill the pool.