Related Topics: More Geometry Lessons

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 = 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

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 pi?**

### Surface area of a hollow cylinder

= 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}

### 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.

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.

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

where r is the radius and h is the height.

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 cmSurface area = 2πr (r + h)

=

= 528 cm

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

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(πR

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

= 40π + 48π + 3.52π

= 91.52π

= 91.52 × 3.142

= 287.56 cm

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

Find the surface area of a cylinder without the lid.

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