Problem Solving

Hi All,

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 can be solved by TESTing VALUES.

Volume of a cube = (Side)^3
Volume of a cylinder = (pi)(Radius^2)(Height)

IF....
the edge of a cube is 2, then its volume is (2)^3 = 8
the radius of the cylinder would be 2/2 = 1
and the height of the cylinder would be 2.
Thus, the volume of the cylinder would be (pi)(1^2)(2) = 2pi and the ratio of the volumes would be 8:2pi = 4:pi

Final Answer: C

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

AAPL wrote:Princeton Review

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 cylinder?

$$\text{A. }\frac{2}{\pi}$$
$$\text{B. }\frac{\pi}{4}$$
$$\text{C. }\frac{4}{\pi}$$
$$\text{D. }\frac{\pi}{2}$$
$$\text{E. }4$$

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^3Ï€/4

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

x^3/(x^3Ï€/4)

1/(Ï€/4)

4/Ï€

Answer: C