Dominic S. answered • 11/02/15

Math and Physics Tutor

The formula for the surface area of a cylinder with radius r and height h is:

A = 2πr

^{2}+ 2πrh; conceptually, the first half of this represents the top and bottom circles on the cylinder, while the second represents the 'body' of it. We can also simplify it a trifle as A = 2πr(r + h)Since we know the area and radius, we can use this formula to find the height:

54π = 2π(3)(3+h)

54 = 6(3+h)

9 = 3+h

h = 6

So the cylinder is 6 cm tall.

The volume of a cylinder, meanwhile, can be calculated as V = πr

^{2}h, which is just the area of one circular end times the height. Plugging in the radius and height gives usV = π(3*3)6 = 54π cm

^{3}. By coincidence, it comes out numerically the same as the surface area, though it has different units (centimeters cubed instead of squared) - in general, the volume and surface area isn't going to be the same number.