Kids Math
Finding the Volume and Surface Area of a Cylinder
What is a cylinder?
There are different kinds of cylinders. On this page we will be discussing the most simple form where the cylinder looks like a tube or a soup can with two circles at each end that are the same size and parallel.
Terms of a Cylinder
In order to calculate the surface area and volume of a cylinder we first need to understand a few terms:
Radius  The radius is the distance from the center to the edge of the circles at each end.
Pi  Pi is a special number used with circles. We will use an abbreviated version where Pi = 3.14. We also use the symbol π to refer to the number pi in formulas.
Height  The height or length of the cylinder.
Surface Area of a Cylinder
The surface area of a cylinder is the surface area of both circles at each end plus the surface area of the outside of the tube. There is a special formula used to figure this out.
Surface area = 2πr^{2} + 2πrh
r = radius
h = height
π = 3.14
This is the same as saying (2 x 3.14 x radius x radius) + (2 x 3.14 x radius x height)
Example:
What is the surface area of a cylinder with radius 3 cm and height 5 cm?
Surface area = 2πr^{2} + 2πrh
= (2x3.14x3x3) + (2x3.14x3x5)
= 56.52 + 94.2
= 150.72 cm^{2}
Volume of a Cylinder
There is special formula for finding the volume of a cylinder. The volume is how much space takes up the inside of a cylinder. The answer to a volume question is always in cubic units.
Volume = πr^{2}h
This is the same as 3.14 x radius x radius x height
Example:
Find the volume of a cylinder with radius 3 cm and height 5 cm?
Volume = πr^{2}h
= 3.14 x 3 x 3 x 5
= 141.3 cm ^{3}
Things to Remember
 Surface area of a cylinder = 2πr^{2} + 2πrh
 Volume of a cylinder = πr^{2}h
 You need to know the radius and height to figure both the volume and surface area of a cylinder.
 Answers for volume problems should always be in cubic units.
 Answers for surface area problems should always be in square units.
More Geometry Subjects
Circle
Polygons
Quadrilaterals
Triangles
Pythagorean Theorem
Perimeter
Slope
Surface Area
Volume of a Box or Cube
Volume and Surface Area of a Sphere
Volume and Surface Area of a Cylinder
Volume and Surface Area of a Cone
Angles glossary
Figures and Shapes glossary
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