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

## Example Questions

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

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

32π cm2

40π cm2

56π cm2

36π cm2

48π cm2

48π cm2

Explanation:

SAcylinder = 2πrh + 2πr2 = 2π(2)(10) + 2π(2)2 = 40π + 8π = 48π cm2

### Example Question #27 : Cylinders

If a cylinder has a radius, , of 2 inches and a height, , of 5 inches, what is the total surface area of the cylinder?

Explanation:

The total surface area will be equal to the area of the two bases added to the area of the outer surface of the cylinder. If "unwrapped" the area of the outer surface is simply a rectangle with the height of the cylinder and a base equal to the circumference of the cylinder base. We can use these relationships to find a formula for the total area of the cylinder.

Use the given radius and height to solve for the final area.

### Example Question #28 : Cylinders

The volume of a cylinder is . If the radius of the cylinder is three, what is the surface area of the cylinder?

Explanation:

The volume of a cylinder is equal to:

Use this formula and the given radius to solve for the height.

Now that we know the height, we can solve for the surface area. The surface area of a cylinder is equal to the area of the two bases plus the area of the outer surface. The outer surface can be "unwrapped" to form a rectangle with a height equal to the cylinder height and a base equal to the circumference of the cylinder base. Add the areas of the two bases and this rectangle to find the total area.

Use the radius and height to solve.

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

What is the surface area of a cylinder with a base diameter of  and a height of ?

Explanation:

Area of a circle

Circumference of a circle

Surface area of a cylinder

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

What is the surface area of a cylinder with a radius of  and a height of ? Give your answer in terms of .

Explanation:

To find the surface area of a cylinder with radius  and height  use the equation:

Thus for a cylinder with a radius of 5 and a height of 7 we get:

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

A cylindrical grain silo is erected vertically, to rest on one of its faces. The silo is then covered with reflective paint. If the cylinder is  tall and has a circumference of , how many square meters of paint must be used? (We'll assume the first coat is enough.)

Explanation:

The formula for the surface area of a cylinder is:

, where  is the circumference of the cylinder and  is the height.

In this case, we must also remember not to include one of the two  measurements, since the bottom face will not be painted. So our modified formula will be:

Since the circumference is , we know the radius is , as

Plug in all these values to the equation to solve for the paintable surface area.

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

Find the surface area of a cylinder whose height is 6 and radius is 7.

Explanation:

To solve, simply use the formula for surface area of a cylinder.

First, identify all known information.

Height = 6