### All ACT Math Resources

## 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?

**Possible Answers:**

48π cm^{2 }

32π cm^{2 }

40π cm^{2 }

36π cm^{2 }

56π cm^{2 }

**Correct answer:**

48π cm^{2 }

SA_{cylinder} = 2πrh + 2πr^{2} = 2π(2)(10) + 2π(2)^{2} = 40π + 8π = 48π cm^{2}

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

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

**Possible Answers:**

**Correct answer:**

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

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

**Possible Answers:**

**Correct answer:**

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 #2 : 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 ?

**Possible Answers:**

None of the answers

**Correct answer:**

Area of a circle

Circumference of a circle

Surface area of a cylinder

### Example Question #3 : 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 .

**Possible Answers:**

**Correct answer:**

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

**Add an image of a cylinder and mark its height and radius (maybe indicate that it is on the ground or a horizontal plane)**

A grain silo in the shape of a right circular cylinder is erected vertically, as shown below. 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 to completely cover the visible portions of the silo in one coat of paint?

**Possible Answers:**

**Correct answer:**

The surface area of a cylinder can be calculated using the following formula:

In this equation, the variable, , 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 that is in contact with the ground will not be painted. We need to modify our surface area formula in the following way:

We are given the circumference of the cylinder; therefore, we can use this information to solve for the radius.

Since the circumference is , we know the radius is 3. Now, we can insert these values to the modified surface area equation and solve for the paintable surface area of the silo.

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

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

**Possible Answers:**

**Correct answer:**

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

First, identify all known information.

Height = 6

Radius = 7

Substitute these values into the surface area equation and solve.

Thus,

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