If the volume of a cube is 8, what is the shortest distance from the center of the cube to the base of the cube?

(A) 1
(B) 2
(C) 3
(D) 2√ 2 
(E) 2√ 3 

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Answer:

Choice A
Level of Difficulty E M H

It will help to draw a simple 3D cube on your paper using the simple technique of drawing two squares, one slightly displaced from the other both vertically and horizontally, then connecting the four corners.

Draw a dot at the center of the cube, then draw a line straight down to the base, the shortest possible distance to the base of the cube. If you consider the equation for the volume of a cube,

volume = side3

it's easy to calculate the length of the side of the cube by plugging 8 in for the volume and taking the cube root of both sides, giving a length of 2. From there, it should be fairly obvious that the length of the line you drew is 1, since it goes halfway down the length of the cube, from the center to the base. This is choice A.

For more practice with 3D solids, go to Skill Set 12: Geometry - 2D Figures and 3D Solids.

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