Bunuel wrote:
The largest possible cube is enclosed in a cylinder and has volume 64. What is the volume of the cylinder if its height is 12?
A. 384π
B. 192π
C. 144π
D. 96π
E. 48π
The volume of a sphere is given by Side^3 = 64
So Side = 4
When a largest possible cube is enclosed in a cylinder, the diagonal of the bottom face of the cube will be the diameter of the cylinder.
Diagonal of the bottom face = \(4*\sqrt{2}\)
So radius of the cylinder = \((4*\sqrt{2})/2 = 2\sqrt{2}\)
Volume of the cylinder = \(\pi*r^2 * h = \pi * (2\sqrt{2})^2 * 12 = 96\pi\)
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Karishma
Veritas Prep GMAT Instructor
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