http://www.ck12.org Chapter 11. Surface Area and Volume
Surface Area
Surface areais the sum of the areas of the faces. Let’s find the net of a right cylinder. One way for you to do this
is to take a label off of a soup can or can of vegetables. When you take this label off, we see that it is a rectangle
where the height is the height of the cylinder and the base is the circumference of the base. This rectangle and the
two circular bases make up the net of a cylinder.
From the net, we can see that the surface area of a right cylinder is
(^2) ︸ π︷︷r ︸^2 + (^2) ︸︷︷︸πrh
area of length
both of
circles rectangle
Surface Area of a Right Cylinder:Ifris the radius of the base andhis the height of the cylinder, then the surface
area isSA= 2 πr^2 + 2 πrh.
To see an animation of the surface area, click http://www.rkm.com.au/ANIMATIONS/animation-Cylinder-Surface-
Area-Derivation.html , by Russell Knightley.
Volume
Volumeis the measure of how much space a three-dimensional figure occupies. The basic unit of volume is the
cubic unit: cubic centimeter(cm^3 ), cubic inch(in^3 ), cubic meter(m^3 ), cubic foot(f t^3 ), etc. Each basic cubic unit
has a measure of one for each: length, width, and height. The volume of a cylinder isV= (πr^2 )h, whereπr^2 is the
area of the base.
Volume of a Cylinder:If the height of a cylinder ishand the radius isr, then the volume would beV=πr^2 h.