A cylindrical shaped oil tank has a diameter of 6 inches and holds 26 pounds of oil. What is the total surface area of this tank? (Hint: Find the volume of the tank first. Then find the height of the tank. The total surface area is the sum of the areas of the two end caps and an area of a rectangle formed by the tank height and the circumference of the end cap.)



Answer :

Answer:

For  the cylinder:
V  = πr²h

d = 6
r = 3 inches

V  = πr²h
V  = πr3²h

V  = 9πh

Given data:
Since the tank holds 26 pounds of oil:

V = 26
26  = 9πh
[tex]h = \frac{26}{9\pi}[/tex]

Total area (At):

At = 2Ab + Al
Where:
Ab:  base area
Al : lateral area

Calculating Ab
Ab =πr²
Ab = π3²
Ab = 9π in²

Al = 2πrh
[tex]Al = \frac{2\pi \times 3 \times 26}{9\times \pi} \\ \\ \\Al = \frac{2\times 3 \times 26}{9} \\ \\ \\Al = \frac{52}{3}[/tex]

Calculating At:

At = 2Ab + Al
At = 2×9π +  52/3


At = 18π +  52/3