In these lessons, we will learn

- 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 Pages**

Surface Area Formulas

Surface Area of Prisms

Surface Area of a Sphere

More Geometry Lessons

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 = 2πr^{2} + 2πrh = 2πr(r + h)

where r is the radius and h is the height.

**Worksheets**

Calculate the volume of cylinders

Calculate the surface area of cylinders

Volume and surface area of cylinders

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 cm^{2}

**How to derive and use the formula of the surface area of a cylinder?**

**How to find the surface area of a cylinder?**

**Example:**

Find the surface area of a cylinder with r = 18in, h = 17in.

**How to calculate the surface area of a cylinder in terms of π?**

Hollow cylinders like pipes or tubes have internal surfaces to consider.

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(πR^{2}– πr^{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}

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

Find the surface area of a cylinder without the lid.

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

Try the free Mathway calculator and
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