Question

An oil company is considering adding a more environmentally friendly grade of fuel at its service stations. To do this, an additional 3600-gallon tank must be buried at each station. Discussions with tank fabricators indicate that the least expensive tank would be cylindrical with minimum surface area. What size tank should be ordered

Answer 1

Given number of gallon tank = 3600

We have to find the size of tank that should be ordered.

Explanation:

Since we know that, 1 gallon = 0.133681 ft^3

3600 gallons = 481.25 ft^3

Volume = πr^2 h

πr^2 h = 481.25

h = 481.25 / πr^2

Surface are = 2πrh + 2πr^2

Now insert values, A = 2πr (481.25 / πr^2) + 2πr^2

A = 2πr (481.25 / πr^2) + 2πr^2

A = 962.5 / r + 2πr^2

For minimum surface area.

dA / dr = 0

962.5 / r^2 + 4πr = 0

962.5 / r^2 = 4πr

962.5 = 4πr^3

r^3 = 76.56

r = 4.25

The radius of cylinder = 4.25 ft

Height = 481.25 / πr^2

Height = 481.25 / π(4.25)^2

Height = 8.48 ft.