Surface Area of a Cylinder

In this lesson, we will learn how to

• calculate the surface area of solid cylinders.
• calculate the surface area of hollow cylinders.
• solve word problems about cylinders.
• calculate the surface area of cylinders using nets.

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.

Worksheet to calculate volume of cylinders.
Worksheet to calculate surface area of cylinders.
Worksheet to calculate volume and surface area of cylinders.
Worksheet to calculate surface area of cylinders and pipes.

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

Surface area of a hollow cylinder

Sometimes you may be required to calculate the total surface area of a hollow cylinder or tube.

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

This video shows how to derive 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.

Word problems about cylinders

Problem: How many square feet of metal are used to make the can?

Problem: Find the surface area of a paint can

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.

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