Finding the surface area of a cylinder.

Question

If the surface area of a cylinder with a radius of 3 cm is 54(pie) cm^2 , what is the cylinder's volume?

Answer 1

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

 

A = 2πr² + 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 = πr²h, which is just the area of one circular end times the height.  Plugging in the radius and height gives us

 

V = π(3*3)6 = 54π cm³.  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.