Question

The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 3   ft long with a diameter of 2.4   ft . Suppose gas is poured into the tank at a rate of 2.5   ft 3 per minute. How many minutes does it take to fill the empty tank? Use the value 3.14 for π , and round your answer to the nearest minute. Do not round any intermediate computations.

Answer 1

the diameter of the gas tank is 2.4, that means the radius is half that, or 1.2, check the picture below.

now, the tank is filling up at 2.5 ft³/min

how many times is 2.5 into V?


`\bf V=\pi ft \cdot 1.2^2 ft\cdot 3 ft\implies 4.32\pi\ ft^3 \\\\\\ \textit{the rate is filling up is }2.5(ft^3)/(min) \\\\\\ \cfrac{4.32\pi \ ft^3}{(2.5\ ft^3)/(min)}\implies \cfrac{(4.32\pi \ ft^3)/(1)}{(2.5\ ft^3)/(min)}\implies \cfrac{4.32\pi \ ft^3}{1}\cdot \cfrac{min}{2.5\ ft^3}\implies \cfrac{4.32\pi }{2.5}min`

that many minutes, round it away.

Answer 2

Find out the volume of the cylinder using the formula for the volume of a cylinder. When you do that, you get that the volume of the tank, when it's full, is 4.5216 ft^3. If the tank is being filled at a rate of 2.5 ft^3 per minute, just divide the total volume by 2.5 to get that, after rounding, it takes 2 minutes to fill the tank. 1.80864 before rounding.