The largest possible cube with volume x is enclosed in a cylinder, what is the volume of the cylinder?
(1) The area of the base of the cylinder is 8Ï€.
(2) x is 64
For any square with side s, diagonal = s√2.
Statement 1:
πr² = 8π
r = √8 = 2√2, implying that d = 4√2.
Thus, the base of cylinder looks like this:
The square represents the base of the largest cube that can be enclosed in a cylinder with a base of 8Ï€.
Since the diagonal of the square = 4√2, s = 4.
Thus, the largest possible cube has an edge of length 4, implying a volume of 64.
Case 1:
Case 2:
Cases 1 and 2 illustrate that the cylinder can have different heights.
Thus, the volume of the cylinder cannot be determined.
INSUFFICIENT.
Since Cases 1 and 2 also satisfy statement 2, the two statements combined are INSUFFICIENT to determine the volume of the cylinder.
The correct answer is
E.
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