In these lessons, we will learn how to

### 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.

Surface area = 2 × area of circle + area of rectangle

Surface Area = 2π*r*^{2} + 2π*rh* = 2π*r*(*r + h*)

where*r* is the radius and *h* is the height.

Surface area = 2π*r* (*r* + *h*)

=

= 528 cm^{2}

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

= area of internal surface + area of external surface + area of the two rings

= 2π*rh* + 2π*Rh* + 2(π*R*^{2}– π*r*^{2})

= (2π × 2 × 10) + (2π × 2.4 × 10) + (2 × (2.4^{2}π – 2^{2}π))

= 40π + 48π + 3.52π

= 91.52π

= 91.52 × 3.142

= 287.56 cm^{2}

### 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.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

- 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.

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 = 2π

where

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 cmSurface area = 2π

=

= 528 cm

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

= area of internal surface + area of external surface + area of the two rings

= 2π

= (2π × 2 × 10) + (2π × 2.4 × 10) + (2 × (2.4

= 40π + 48π + 3.52π

= 91.52π

= 91.52 × 3.142

= 287.56 cm

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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