In these lessons, we will learn how to
- calculate the surface area of solid cylinders.
- calculate the surface area of hollow cylinders or tubes or pipes.
- solve word problems about cylinders.
- calculate the surface area of cylinders using nets.
Related Topics: More Geometry Lessons
Surface Area of a Solid Cylinder
A cylinder is a solid that has two parallel faces which are congruent circles
. These faces form the bases
of the cylinder. The cylinder has one curved surface
. The height
of the cylinder is the perpendicular distance between the two bases.
The net of a solid cylinder consists of 2 circles and one rectangle. The curved surface opens up to form a rectangle.
Surface area = 2 × area of circle + area of rectangle
Surface Area = 2πr2
(r + h
is the radius and h
is the height.
The diameter of the base of a cylinder is 12 cm and the height is 8 cm. Find the surface area of the solid cylinder.
Radius = 6 cm
Surface area = 2πr
= 528 cm2
This video shows how to derive and use the formula of the surface area of a cylinder.
The following video shows how to find the surface area of a cylinder.
This video illustrates how to calculate the surface area of a cylinder in terms of pi.
Surface area of a hollow cylinder
Sometimes you may be required to calculate the total surface area of a hollow cylinder or tube or pipe.
Total surface area of hollow cylinder
= area of internal curved surface + area of external curved surface + area of the two rings
The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the total surface area of the pipe
r = 2, R = 2.4, h = 10
Total surface area of pipe
= area of internal surface + area of external surface + area of the two rings
= (2π × 2 × 10) + (2π × 2.4 × 10) + (2 × (2.42
π – 22
= 40π + 48π + 3.52π
= 91.52 × 3.142
= 287.56 cm2
Word problems about cylinders
Problem: How many square feet of metal are used to make the can?
Problem: Find the surface area of a cylinder without the lid.
Surface Area of cylinder using nets
Use the net of a cylinder to determine its volume and surface area.
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