Final answer:
To determine how long the circular pool will take to drain, calculate the volume using the formula for the volume of a cylinder and then divide by the drainage rate. The pool has a volume of approximately 15,904 cubic inches and will take about 69.15 minutes to drain at a rate of 230 cubic inches per minute.
Step-by-step explanation:
To calculate the time it will take for the circular pool to be completely drained, we must first determine the volume of the pool and then how long it will take to drain it at a rate of 230 cubic inches per minute. Given that the pool is 10 inches deep with a 45 inches diameter, we can use the formula for the volume of a cylinder ∙ V = πr^2h, where V is the volume, r is the radius, and h is the height or depth of the pool.
First, calculate the radius of the pool, which is half the diameter: r = 45 inches / 2 = 22.5 inches. Then, calculate the volume of the pool: V = π * (22.5 inches)^2 * 10 inches. Calculating this gives us the volume V as approximately 15,904 inches^3.
Now, with the draining rate of 230 cubic inches per minute, we can estimate the time to drain the pool by dividing the total volume by the rate: Time = Volume / Rate. The calculation is Time = 15,904 inches^3 / 230 inches^3/min, resulting in approximately 69.15 minutes to drain the pool.