If the radius of a cylinder is half the . . . .

Hi VJesus12,

We're told that the radius of a cylinder is half the length of the edge of a cube and the height of the cylinder is equal to the length of the edge of the cube. We're asked for the ratio of the volume of the cube to the volume of the cylinder. This question requires a couple of formulas and can be solved by TESTing VALUES.

IF....
Side of the cube = 2
Radius of the cylinder = 1
Height of the cylinder = 2

Volume of the cube = (side)^3 = (2)^3 = 8
Volume of the cylinder = (pi)(R^2)(H) = (pi)(1^2)(2) = 2pi

Ratio of cube volume to cylinder volume = 8:2pi = 4:pi

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

VJesus12 wrote:If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?

A. 2/Ï€

B. π/4

C. 4/Ï€

D. π/2

E. 4

We can let x = the length of the edge of the cube. Thus, the volume of the cube is x^3. Furthermore, the radius of the cylinder is x/2, and the height of the cylinder is x. Since the volume of a cylinder is V = πr^2h, the volume of the cylinder is:

V = π(x/2)^2 * x

V = π(x^2/4) * x

V = x^3 * π/4

Thus, the ratio of the volume of the cube to that of the cylinder is:

x^3/(x^3 * π/4)

1/(Ï€/4)

4/Ï€

Answer: C