Question

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

Answer 1

8 minutes

Step-by-step explanation

To find how long will it take to fill the empty tank, we have to find what is the volume of the tank first. We know that the tank is a cylinder 3 feet long with a diameter of 2.2 ft, so its volume is given by,

`V=\pi r^2h`

Where h is the length of the tank and r is its radius - which is half the diameter, so r = 1.1 ft. The volume of the tank, if we use 3.14 for π, is,

`V=3.14\cdot1.1^2ft^2\cdot3ft=11.3982ft^3`

We know that the gas is poured into the tank at a rate of 1.5 ft³/min, so for a volume of 11.3982 ft³, the time it will take to fill the tank is,

`t=(11.3982ft^3)/(1.5ft^3/min)=7.5988min\approx8min`

Hence, it will take 8 minutes to fill the empty tank, rounded to the nearest minute.