Volume of a Cylinder is defined by: V = Bh where B = the area of the base of the cylinder(area of the circular bottom and top), and h = the distance between the top circle and bottom circle of the cylinder.
To find the radius, we substitute the given information into the formula and solve for "r".
[tex]2916= \pi ( r^{2} )(36)[/tex]
[tex] \frac{2916}{36 \pi } = r^{2} [/tex]
[tex] \frac{81}{ \pi } = r^{2} [/tex]
[tex] \frac{9}{ \sqrt{ \pi } } = r[/tex]
Now, to find the surface area of the tank use S.A. = 2B + π · d · h where B = the area of the circular base, d = the diameter of the circular base, and h = the height of the cylinder.
[tex]SA = 2 \pi ( \frac{9}{ \sqrt{ \pi } }) ^{2} + \pi ( \frac{18}{ \sqrt{ \pi } })(36) [/tex]
[tex][tex]SA = 2 \pi ( \frac{81}{ \pi } }) + \pi ( \frac{648}{ \sqrt{ \pi } })
[/tex]
Now simplifying the first term of the expression on the right and rationalizing the denominator of the second term we get:
[tex][tex]SA = 162 + 648 \sqrt{ \pi }
[/tex]
Hopefully this helps.. let me know if you have questions.
