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# Surface Area of Cylinders II

Lesson

Like finding the surface area of a prism the surface area of a cylinder uses a similar process.

Let's see how it would look if we open up a cylinder to view its net.

Notice that when the curved surface is unfolded, it becomes a rectangle. By rotating the circle on top of the rectangle, can you see how the circumference of the circle is equal to the length of the rectangular piece?

This means that we can break down the total surface area of a cylinder in the following way:

Surface Area of a Cylinder = Area of 2 circular ends  + Area of 1 rectangular piece

= $\left(2\times\pi r^2\right)+\left(L\times W\right)$(2×πr2)+(L×W)

Area of each circle: the radius of each circle is the same as the radius of the cylinder

Area of the rectangle: the width of the rectangle corresponds to the height of the prism, while the length of the rectangle is the circumference of the circle ( $2\pi r$2πr )

Surface Area of a Cylinder

$\text{Surface Area of a Cylinder }=2\pi r^2+2\pi rh$Surface Area of a Cylinder =2πr2+2πrh

#### Worked Examples

##### Question 1

A cylindrical can of radius $7$7 cm and height $10$10 cm is open at one end. What is the external surface area of the can correct to two decimal places?

##### Question 2

Find the exact surface area of a cylinder with diameter $6$6 cm and height $21$21 cm by leaving your answer in terms of $\pi$π.

##### Question 3

Consider the solid pictured and answer the following: 1. What is the external surface area of the curved surface?

2. What is the total surface area of the two end pieces?