To determine how the volumes of the two boxes are related, we can compare the volumes based on the dimensions given.
Let the side length of the first box be \( s \). The volume \( V_1 \) of the first box is given by the formula for the volume of a cube:
\[ V_1 = s^3 \]
The sides of the second box are each \(\frac{1}{3}\) of the sides of the first box. Thus, the side length of the second box is
\[ s_2 = \frac{1}{3}s. \]
The volume \( V_2 \) of the second box is then:
\[ V_2 = \left(\frac{1}{3}s\right)^3 = \frac{1}{3^3}s^3 = \frac{1}{27}s^3. \]
Now, we can compare the two volumes:
\[ \frac{V_2}{V_1} = \frac{\frac{1}{27}s^3}{s^3} = \frac{1}{27}. \]
Thus, the volume of the second box is \(\frac{1}{27}\) of the volume of the first box.
Therefore, the correct answer is:
B. The volume of the second box is \(\frac{1}{27}\) of the volume of the first box.
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