An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4 ft long with a diameter of 2.2 ft. Suppose oil is drained at a rate of 2.3 ft3 per minute. If the tank starts completely full, how many minutes will it take to empty the tank?Use the value 3.14 for π, and round your answer to the nearest minute. Do not round any intermediate computations.
Question
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4 ft long with a diameter of 2.2 ft. Suppose oil is drained at a rate of 2.3 ft3 per minute. If the tank starts completely full, how many minutes will it take to empty the tank?Use the value 3.14 for π, and round your answer to the nearest minute. Do not round any intermediate computations.
Solution
To solve this problem, we first need to find the volume of the cylindrical oil tank. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height (or in this case, the length of the cylinder).
Step 1: Convert the diameter to radius. The radius is half of the diameter, so r = 2.2 ft / 2 = 1.1 ft.
Step 2: Substitute the radius and the length into the volume formula: V = π(1.1 ft)²(4 ft) = 3.14 * 1.21 ft² * 4 ft = 15.16 ft³.
Step 3: Now that we know the volume of the tank, we can find out how long it will take to empty it. If the tank is drained at a rate of 2.3 ft³ per minute, we divide the total volume by the rate of drainage: 15.16 ft³ / 2.3 ft³/min = 6.59 minutes.
Step 4: Round the result to the nearest minute. So, it will take approximately 7 minutes to empty the tank.
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