Question

A cube with $3$ -inch edges is made using $27$ cubes with $1$ -inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?

$\dfrac{1}{9}$

$\dfrac{1}{4}$

$\dfrac{4}{9}$

$\dfrac{5}{9}$

$\dfrac{19}{27}$

Solution:

Since each face has the same black and white surface area, we can analyze what fraction of one side is white.

On one side, there are $9$ unit squares. $4$ of them are black. This means that $\dfrac{5}{9}$ of each face is white.

Thus, D is the correct answer.

2006 AMC 8 Problem 18

Solution:

Problem 18 in Other Years