Question

A gas station has a cylindrical fueling tank that holds the gasoline for its pumps, as modeled below. The tank holds a maximum of 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 ]

Answer 1

Answer:

$\boxed{ \text{10.9 ft}}$

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 = $\boxed{ \textbf{10.9 ft}}$