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 )
$\text{Surface Area of a Cylinder }=2\pi r^2+2\pi rh$Surface Area of a Cylinder =2πr2+2πrh
Worked Examples
QUESTION 1
Consider the following cylinder with a height of $35$35 cm and base radius of $10$10 cm. Find the surface area of the cylinder.
A vertical cylinder with a dashed circle at the bottom indicating the base, which is hidden from view. A solid line circles the top, representing the visible base. Two measurements are shown: a horizontal line from the center of the circle to the circumference measuring $10$10cm above the top base, implying the radius, and a vertical dimension line adjacent to the right side of the cylinder measuring $35$35cm indicating the height.
Round your answer to two decimal places.
QUESTION 2
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?