Final answer:
To find out how fast water is draining from the tank, calculate the volume of water lost as the water level drops at a rate of 6 inches per minute. By using the volume formula for a cylinder (πr^2h), with a radius of 1 ft and a height drop of 0.5 ft, the water is draining at about 1.57 cubic feet per minute.
Step-by-step explanation:
To calculate how fast water is draining out of the tank, we need to find the volume of water being drained per unit time. The rate at which the water level is dropping is 6 inches per minute, and since there are 12 inches in a foot, this is equivalent to 0.5 feet per minute. The volume of a cylinder is given by the area of the base multiplied by the height, so we can find the volume of water that leaves the tank each minute by calculating the volume of the cylindrical segment that the water occupies as it drops 0.5 feet.
The volume drained per minute, or V, can be determined by the following formula: V = πr^2h, where π is Pi (approximately 3.14159), r is the radius of the tank (1 ft in this case), and h is the change in height per minute (0.5 ft). Plugging in the values, we get: V = π(1 ft)^2(0.5 ft) which simplifies to V = (3.14159 ft^2)(0.5 ft) = Approximately 1.570795 cubic feet per minute.