# Area of Hollow Cylinder: Defining Terms and Cross Sectional Area

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A hollow cylinder is one which is empty from inside and has some difference between the internal and external radius.

Tubes, circular buildings, straws these are all examples of a hollow cylinder.

## Area of a Hollow Cylinder

### Defining Terms

Let be the **outer radius** of the given cylinder and be its **inner radius** and ‘h’ be its **height**.

be the outer circumference and be the inner circumference.

and be the outer and inner surface areas respectively.

t be the thickness of the cylinder

### Area of Hollow Cylinder Formulas

The Circumference of a circle (C) is given by:

therefore,

The Lateral Surface Area for a cylinder is:

therefore,

the external curved surface area

the internal curved surface area

Thus, Lateral Surface Area of a hollow cylinder

### Cross Sectional Area

Let A be the area of a cross-section of a hollow cylinder,

for a circle, therefore,

for the area enclosed by

for the area enclosed by

for the cross-sectional area of hollow cylinder

Total Surface Area of a Hollow Cylinder:

**Example: Find (in** **) the curved surface area of a hollow cylinder with thickness 2 cm external radius 8 cm and height is 20 cm.**

**Solution:**

Let the external radius, internal radius , and height of the hollow cylinder

Here given external radius

Thickness

Internal radius

Height

Here using formula,

Curved surface area of hollow cylinder

We put the value of internal radius, external radius and heights.

Sum of the 8 and 6,

Here 14 divided by 7

Example 2: The external surface area of a hollow cylinder is . Its internal diameter is 16 cm and height 15 cm. Find the curved surface area.

Solution:

Here given, external surface area of a hollow cylinder

Formula of surface area of cylinder

Also given internal radius

Height

Values are put in the equation (1),

Both the side cancel.

2 and 15 take the other side,

First, we divide 540 by 15.

Curved Surface area

Put the value,