GMAT Math : Cylinders
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Example Questions
Example Question #4 : Dsq: Calculating The Volume Of A Cylinder
Which of Cylinder 1 and Cylinder 2, if either, has the greater volume?
Statement 1: The height of Cylinder 1 is equal to the radius of the base of Cylinder 2.
Statement 2: The height of Cylinder 2 is equal to twice the radius of the base of Cylinder 1.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements. We show that insufficient information is provided using two cases.
Case 1: Cylinder 1 has height 10 and radius 20. Then Cylinder 2 has height 40 and radius 10.
The volume of Cylinder 1 is
The volume of Cylinder 2 is
Case 2: Cylinder has height 40 and radius 10. Then Cylinder 2 has height 20 and radius 40.
The volume of Cylinder 1 is
The volume of Cylinder 2 is
In one case, Cylinder 1 had greater volume; in the other, Cylinder 2 did. This makes the two statements insufficient.
Example Question #212 : Geometry
How many identical cans can be packed in a certain box?
(1) The box is 
(2) Each can is 
E: Statements (1) and (2) TOGETHER are not sufficient
D: EACH statement ALONE is sufficient
C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
A: Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient
B: Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient
E: Statements (1) and (2) TOGETHER are not sufficient
(1) does not give us any information about the cans' dimension or the length of the box, so it is not sufficient alone.
(2) does not give us box dimensions or any information about the cans' diameter, so it is not sufficient alone.
Both statement taken together give more information but we still dont have complete dimensions for the box or each can.
Therefore the right answer is E.
Example Question #213 : Geometry
Jenkins has a poster tube which he is using to carry his posters to college.
I) The poster tube has a volume of 
II) The poster tube is 
What is the radius of the poster tube?
Either statement alone is sufficient to answer the question.
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Neither I nor II are sufficient to answer the question. More information is needed.
Both statements are necessary to answer the question.
Both statements are necessary to answer the question.
Recall the formula for volume of a cylinder:
Statement I gives us V
Statement II gives us h
We can then use both of them to find our "r." We cannot do it without both of them.
Example Question #1 : Dsq: Calculating The Volume Of A Cylinder
How much water, in cubic feet, can a cylindrical water tank whose bases have radius 6 feet hold?
Statement 1: The lateral area of the tank is 125.66 square yards.
Statement 2: The tank is 30 feet high.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
We are given the radius; if we know the height, we can use the formula
to calculate the volume of the tank.
The second statement gives us that the tank is 30 feet high. But the first statement gives us the way to find the height by using the lateral area formula.
First we have to convert square yards to square feet by multiplying by 9.
Either way, we now have both radius and height, and we can find the volume:
The answer is that either statement alone is sufficient to answer the question.
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