A gas station has a cylindrical fueling tank that holds the gasoline for its pumps, as modeled below. The tank holds a maximum o
f 20,000 gallons of gasoline and has a length of 34.5 feet.
A metal pole is used to measure how much gas is in the tank.
To the nearest tenth of a foot, how long does the pole need to be in order to reach the bottom of the tank and still extend one foot outside the tank?
[1 ft^3=7.48 gallons ]
A metal pole is used to measure how much gas is in the tank.
To the nearest tenth of a foot, how long does the pole need to be in order to reach the bottom of the tank and still extend one foot outside the tank?
[1 ft^3=7.48 gallons ]
1 answer:
Answer:
Step-by-step explanation:
The formula for the volume of a cylinder is
V = πr²h
Data:
V = 20 000 gal
h = 34.5 ft
Calculations:
I assume the gasoline tank is lying on its side, so we are asked to find the diameter of the tank.
(a) Convert the volume to cubic feet
V= 20 000 gal × (1 ft³/7.48 gal) = 2674 ft³
(b) Calculate the radius of the tank
V = πr²h
r² = V/(πh) = 2674/(π × 34.5) = 24.67 ft²
r = √24.67 = 4.967 ft
(c) Calculate the diameter of the tank
d = 2r = 9.934 ft
(d) Calculate the length of the measuring pole
l = d + 1 = 9.934 + 1 =
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