How to find the surface area of a cylinder - ISEE Upper Level (grades 9-12) Quantitative Reasoning
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What is the surface area of a cylinder of height 
in., with a radius of 
in?
What is the surface area of a cylinder of height
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:
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:
Compare your answer with the correct one above
What is the surface area of a cylinder having a base of radius 
in and a height of 
in?
What is the surface area of a cylinder having a base of radius
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:
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:
Compare your answer with the correct one above
What is the surface area of a cylinder with a height of 
in. and a diameter of 
in?
What is the surface area of a cylinder with a height of
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:
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
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:
Compare your answer with the correct one above
The volume of a cylinder with height of 
is 
. What is its surface area?
The volume of a cylinder with height of
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:
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:
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
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:
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:
Compare your answer with the correct one above
What is the surface area of a cylinder of height in, with a radius of in?
What is the surface area of a cylinder of height
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:
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:
Compare your answer with the correct one above