# High School Math : How to find the surface area of a cylinder

## Example Questions

### Example Question #95 : Solid Geometry

This figure is a right cylinder with radius of 2 m and a height of 10 m.

What is the surface area of the right cylinder (m2)?

Explanation:

In order to find the surface area of a right cylinder you must find the area of both bases (the circles on either end) and add them to the lateral surface area.  The area of the two circles is easy to find with but remember to multiply by 2 for both bases

.

Next find the lateral area.  The lateral area if unrounded would be a rectangle with height of 10 m and length equal to the circumference of the base circles. Thus the lateral area is

Now add the lateral area to the area of the two bases:

### Example Question #96 : Solid Geometry

Find the surface area of a cylinder given that its radius is 2 and its height is 3.2.

Explanation:

The standard equation to find the surface area of a cylinder is

where  denotes the radius and  denotes the height.

Plug in the given values for  and  to find the area of the cylinder:

### Example Question #97 : Solid Geometry

The base of a cylinder has an area of  and the cylinder has a height of . What is the surface area of this cylinder?

Explanation:

The standard equation for the surface area of a cylinder is

where  denotes radius and  denotes height. We've been given the height in the question, so all we're missing is the radius. However, we are able to find the radius from the area of the circle:

We know the area is

so

Now that we have both  and , we can plug them into the standard equation for the surface area of a cylinder:

### Example Question #1 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following cylinder.

Explanation:

The formula for the surface area of a cylinder is:

where  is the radius of the base and  is the length of the height.

Plugging in our values, we get:

### Example Question #99 : Solid Geometry

Find the surface area of the following cylinder.

Explanation:

The formula for the surface area of a cylinder is:

Where  is the radius of the cylinder and  is the height of the cylinder

Plugging in our values, we get:

### Example Question #1 : Cylinders

Find the surface area of the following partial cylinder.

Explanation:

The formula for the surface area of this partial cylinder is:

Where  is the radius of the cylinder,  is the height of the cylinder, and  is the sector of the cylinder.

Plugging in our values, we get:

### Example Question #2 : Cylinders

Find the surface area of the following partial cylinder.

Explanation:

The formula for the surface area of this partial cylinder is:

where  is the radius of the cylinder,  is the height of the cylinder, and  is the sector of the cylinder.

Plugging in our values, we get:

### Example Question #1 : Cylinders

What is the surface area of cylinder with a radius of 3 and height of 7?