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Year 9 Interactive Maths - Second Edition


Curved Surface Area of a Cylinder

If a plane cuts a solid parallel to its base, then the exposed surface is said to be a cross-section.

A solid such as a can of drink is a cylinder if its cross-section is a circle.

The radius of the circular cross-section is called the radius of the cylinder, and the straight line that passes through the centre of each circular cross-section is called the axis of the cylinder.  The length of the axis is called the height of the cylinder.  The radius and height of the cylinder are represented by r and h respectively.

Consider a cylindrical can of radius r and height h.

To determine a formula for the curved surface area of a cylindrical can, wrap a sheet of paper snugly around the can and tape it together.  Trim the paper at the top and bottom to match the shape of the can.  Then slide the paper off the can and cut this paper cylinder parallel to its axis so that it forms the rectangle shown in the following diagram.


Just to recap the above discussion:

The curved surface area (CSA) of a cylinder with radius r and height h is given by


Example 23

Find the area of the curved surface of a cylindrical tin with radius 7 cm and height 4 cm.

Solution:


Note:

The circular base of the cylinder is drawn as an ellipse.


Key Terms

plane, cross-section, cylinder, radius of a cylinder, axis of a cylinder, height of a cylinder, curved surface area (CSA)


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