### All ISEE Upper Level Quantitative Resources

## Example Questions

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

What is the surface area of a cylinder of height in., with a radius of in?

**Possible Answers:**

**Correct answer:**

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

For our problem, this is:

You need to double this for the *two* bases:

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

For our problem, this is:

Therefore, the total surface area is:

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

What is the surface area of a cylinder having a base of radius in and a height of in?

**Possible Answers:**

**Correct answer:**

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

For our problem, this is:

You need to double this for the *two* bases:

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

For our problem, this is:

Therefore, the total surface area is:

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

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

**Possible Answers:**

**Correct answer:**

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. Notice, however that the *diameter* is inches. This means that the *radius* is . Now, the equation for one base is:

For our problem, this is:

You need to double this for the *two* bases:

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

For our problem, this is:

Therefore, the total surface area is:

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

The volume of a cylinder with height of is . What is its surface area?

**Possible Answers:**

**Correct answer:**

To begin, we must solve for the radius of this cylinder. Recall that the equation of for the volume of a cylinder is:

For our values this is:

Solving for , we get:

Hence,

Now, recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

For our problem, this is:

You need to double this for the *two* bases:

For our problem, this is:

Therefore, the total surface area is:

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

What is the surface area of a cylinder of height in, with a radius of in?

**Possible Answers:**

**Correct answer:**

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

For our problem, this is:

You need to double this for the *two* bases:

For our problem, this is:

Therefore, the total surface area is:

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