The empty gas tank of the truck needs to be completely filled. The tank is shaped like a cylinder that is 4 feet long with a diameter of 2.4 feet. Suppose gas is poured into the tank at a rate of 1.7 thirds of a foot per minute. How many minutes does it take to fill the empty tank? Use the value 3.14 for pie and round your answer to the nearest minute.
volume = π(1.2)^2 (4) ft^3
rate = 1.7 thirds of a foot ????
once you have that one figured out, divide
volume by rate
To calculate the time it takes to fill the empty tank, we need to find the volume of the cylinder and divide it by the rate at which gas is poured into the tank.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height (or length) of the cylinder.
Given that the diameter of the tank is 2.4 feet, we can find the radius by dividing it by 2: r = 2.4/2 = 1.2 feet.
The height (or length) of the cylinder is given as 4 feet.
Substituting these values into the volume formula, we get V = π(1.2^2)4.
Next, we can calculate the volume: V = 3.14(1.44)(4) = 18.0864 cubic feet (rounded to four decimal places).
Now, we can determine how many cubic feet of gas are poured into the tank per minute. The rate at which gas is poured is 1.7 thirds of a foot per minute, which means 1.7/3 = 0.5667 feet poured per minute.
To find the time it takes to fill the tank, we divide the volume of the tank by the rate at which gas is poured: time = volume/rate = 18.0864/0.5667 ≈ 31.91 minutes.
Rounding to the nearest minute, it takes approximately 32 minutes to fill the empty tank.