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# Surface Area of a Cylinder

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 + 2πrh = 2πr (r + h)

where r is the radius and h is the height.

Example:

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.

Solution:

Radius = 6 cm

Surface area = 2πr (r + h)

=

= 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

Example:

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

Solution:

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
= 2πrh + 2πRh + 2(πR2– πr2)
= (2π × 2 × 10) + (2π × 2.4 × 10) + (2 × (2.42π – 22π))
= 40π + 48π + 3.52π
= 91.52π
= 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.

Problem: The production team has designed this soda can. Determine the amount of aluminum sheet needed to form the can and the amount of soda it will hold.
The diameter of the cylindrical can is 8 cm and the height is 14 cm.
In this video, we find the surface area and volume of a cylinder.

## Surface Area of cylinder using nets

Use the net of a cylinder to determine its volume and surface area.

Use the given net to determine the surface area and volume of the cylinder.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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