A sporting good store sells cylinder shaped weights, and needs to know how much plastic is needed to cover the weights for shipping. The cylinder shaped weights have a diameter of 12 inches, and a height of 8 inches.

SA = Lateral Area + 2 Base areas

SA = pi x 2r x h + 2 pi r^2

SA = pi x 12 x 8 + 2 pi 6^2

SA = 96 pi + 72 pi

SA = 168 pi or 527.52 square inches

The lateral area of a cylinder is 47.1 cm. The height of the cylinder is 6 units. What is the radius of the cylinder?

Lateral Area = pi x 2r x h

47.1 = pi x 2r x 6

47.1/(6 pi) = 2r

2.5 = 2r

1.25 = r

The total surface area of a cylinder is the total area of each of its faces. The formula for calculating the surface area combines each of the following.

- Area of two circular bases

- The circumference of a circle

- The height of the cylinder

To summarize, to find the surface area of a cylinder, take the **area of the two circular bases**, and add this to the **lateral area of the cylinder**.

Helpful worksheets, and example problems in which you calculate the surface area of a cylinder.

Several practice problems,directions,and hints for calculating cylinder surface area.

Great site,sample problems,step by step solutions to many surface area problems

Transcript

Hi Welcome to MooMooMath. Today we are going to talk about the surface area of a cylinder. If you are looking at a can it would be the label of a can, and then the top and bottom lids which are circles so I will divide this into two parts. We will first look at the sides of the soup can if you were to rip the label off. The label actually opens up to form a rectangle. All we have to do is find the area of a rectangle which is length time’s width. The length of the label is the distance around the lid which is the circumference which is d times π and d is your diameter. This side of your can is your height and the sides of your can is your lateral area and d times π times h and that is how you get your lateral area. Now I have to add your top and your bottom of the soup can.The top and bottoms are circles and the area of a circle is just π r squared, and you have two of those so take π r squared plus π r squared or 2πr^2 and that gives me the two bases then I’m going to take the sides and I’m going to add to it the two circles that are bases. So let’s go back and add the whole formula. The formula looks like this: d∙π∙h which is your lateral area plus 2πr^2 so the formula is d∙π∙h + 2πr^2 so let’s look at an example. Say I have a cylinder and the height is 5 and the radius is 2 so we will plug in the diameter would be four because if the radius is 2 the diameter is twice that so take 4 times π and the height is 5 so for my lateral area I will get 20 π. Now let’s add our bases. We need our radius. Let’s go back and we had 2 for the radius so we will take 2 times πr^2 times the radius squared which is 4 and 4 times 2 is 8π and 8 plus 20 is 28 and you stick the π next to it. So that is how you find the surface area. Remember area is 2 dimensional so I will put whatever units it is squared. Because area is two dimensional. So here are the rules. First,add the sides or lateral area plus the two circular bases and the formula is d∙π∙h + 2πr^2 equals the total surface area. Hope this helps.

A

B

C

D

Height = 5 units

Radius = 2 units

Diameter = 2* radius = 2 * 2 =4

Diameter* π*height

4* π*5=20π

20π+ 8π=28π units^2

5

2

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Based on the information presented either of the following formulas will calculate the lateral area of a cylinder.

2πr*h = **2** times** pi** times **radius** times **height**

You can think of the lateral area as the label of a can. It is the area of the sides of the can.

If you unrolled the label you would have a flat surface

d= diameter of the circular base

h= height of the cylinder

r = radius of the circular base