# Intermediate Geometry : How to find the surface area of a cylinder

## Example Questions

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

A cylinder has a volume of 16 and a radius of 4.  What is its height?

Explanation:

Since the radius is 4, the area of the base is .  To cancel out the , the height must be .

### Example Question #2 : How To Find The Surface Area Of A Cylinder

What is the surface area of a cylinder with diameter 4 and height 6? The equation to calculate the surface area of a cylinder is:

Explanation:

If the diameter of the cylinder is 4, the radius is equal to 2. Therefore:

### Example Question #3 : How To Find The Surface Area Of A Cylinder

Find the surface area of the following right cylinder:

Explanation:

The answer is .  To find the surface area we need to find the area of the top, bottom, and the round side respectively.  To find the areas of the top and bottom circles, you would need to use the formula  .

Plug in 4 for , and you get , then multiply by 2 for 2 circles to get

Then to get the area of the round side, you would take the circumference times the height.  Thus with the formula

you would get

Also you could remember the formula

and plug in  and

### Example Question #4 : How To Find The Surface Area Of A Cylinder

Given a cylinder with radius of 5cm and a height of 10cm, what is the surface area of the entire cylinder?

Explanation:

The surface area of the whole cylinder = (2 * area of circle) + lateral area

Think of the lateral area as the paper label on a can; It wraps around the outside of the can while leaving the top and bottom untouched. The area of the circle, times 2, is to account for the top and the bottom of the cylinder.

Area of a circle =

So the area of the circle = , and since there are two circles we have

Now for the lateral area. Notice how if we have a can with a paper label, we can take the label, cut it, and unroll it from the can. In this way, our label now looks like a rectangle with a

height = height and the

width = circumference of the circle.

Circumference =

So our rectangle is going to have a height of 10 and a width of 10. So the lateral area =

So the total surface area =

### Example Question #5 : How To Find The Surface Area Of A Cylinder

The circumference of the base of a cylinder is  and the height of the cylinder is . What is this cylinder's surface area? Round to the tenths place.

Explanation:

The formula to find the surface area of a cylinder is , where  is the height of the cylinder and  is the radius.

In this kind of equation-based problem, it's helpful to ask "What information do I have?" and "What information is missing that I need?"

The problem provides information for the  component of the equation, but not for the  component. Instead, we're given information about the circumference of the circular base of the cylinder. The question that arises now is how the radius can be calculated from the circumference. The formula for circumference is: , where  is diameter. Radius can be calculated by taking half of the diameter. This means that radius and circumference are related in terms of

Therefore, the first step for this problem is to solve for .

Because the diameter is , that means that the radius must be .

Now the surface area can be solved for after the  and  values are substituted into the equation.

### Example Question #6 : How To Find The Surface Area Of A Cylinder

Find the surface area of the cylinder below.

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.

### Example Question #7 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.

### Example Question #8 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.

### Example Question #9 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.

### Example Question #10 : How To Find The Surface Area Of A Cylinder

Find the surface area of the given cylinder.

Explanation:

To find the surface area of the cylinder, first find the areas of the bases:

Next, find the lateral surface area, which is a rectangle:

Add the two together to get the equation to find the surface area of a cylinder:

Plug in the given height and radius to find the surface area.

Make sure to round to  places after the decimal point.

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