Final answer:
To find the radius of the pool, calculate the increase in volume when the 12-liter bucket is emptied into the pool using the formula V = πr²h, where r is the radius of the pool and h is the height the water level rises. By plugging in the known values, the radius of the pool is approximately 38 cm. Therefore, the correct option is a.
Step-by-step explanation:
To find the radius of the pool, we need to calculate the increase in volume when the 12-liter bucket is emptied into the pool. The increase in volume is equal to the volume of water poured into the pool, which can be calculated using the formula:
Volume = πr²h
where r is the radius of the pool and h is the height that the water level rises. Given that the water level rises by 5 millimeters (or 0.005 meters) and the volume is 12 liters (or 0.012 cubic meters), we can substitute these values into the formula:
0.012 cubic meters = πr²(0.005 meters)
Now we can solve for r by rearranging the equation:
r = sqrt(0.012/(π*0.005))
Calculating this value gives us r ≈ 0.379meters. Converting this to centimeters and rounding to the nearest centimeter, the radius of the pool is approximately 38 cm. Therefore, the correct answer is (a) 38 cm.