All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #353 :Geometry
What is the surface area of a cylinder of heightin., with a radius ofin?
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 thetwobases:
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 #354 :Geometry
What is the surface area of a cylinder having a base of radiusin and a height ofin?
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 thetwobases:
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 #355 :Geometry
What is the surface area of a cylinder with a height ofin. and a diameter ofin?
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 thediameterisinches. This means that theradiusis. Now, the equation for one base is:
For our problem, this is:
You need to double this for thetwobases:
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 #1 :Cylinders
The volume of a cylinder with height ofis. What is its surface area?
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 thetwobases:
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 #357 :Geometry
What is the surface area of a cylinder of heightin, with a radius ofin?
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 thetwobases:
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: