The circumference of the bas of the cylinder is 18π units. the cylinder is 30 units tall.
which of the following is the closest to the volume of the cylinder?
a 706 cubic units
b 1,414 cubic units
c 7,630 cubic units
d 21,195 cubic units

The volume of a cylinder is    (pi) (radius)² (height).

We know the height, but we don't know the radius.
Is there a way we can find it ?
We know the circumference of the base.  Maybe that's a clue.
Can you find the radius of a circle when you know the circumference ?

             Circumference of a circle =  (pi) x (diameter)
 
                                    18 pi units = (pi) x (diameter)

Divide both sides by pi :  18 units = diameter

Divide both sides by 2 :    9 units = radius       yay !

Now we know the radius and the height of the cylinder,
so we can calculate the volume.

radius = 9
height = 30
we'll use  3.14  for pi .

Volume = (pi) (radius)² (height) =

             (3.14)    (9)²      (30) =

             (3.14)   (81)      (30) =   7,630.2 cubic units

Is there a choice close to that ?  I'll go up and look.   

Yes !  Choice 'C' is  7,630 cubic units.      yay !

Ithink the correct answer is d.