A larger cube has volume $64 \mathrm{~cm}^{3}$. A smaller cube has edges that are half the length of the edges of the larger cube. What is the volume of the smaller cube?
(A) $24 \mathrm{~cm}^{3}$
(B) $48 \mathrm{~cm}^{3}$
(C) $8 \mathrm{~cm}^{3}$
(D) $16 \mathrm{~cm}^{3}$
(E) $27 \mathrm{~cm}^{3}$
Since a cube is a rectangular prism, its volume is equal to the area of its base, $l \times w$, multiplied by its height, $h$.

A cube has edges of equal length and so $l=w=h$.

Thus, the volume of a cube is the product of three equal numbers.

The volume of the larger cube is $64 \mathrm{~cm}^{3}$ and $64=4 \times 4 \times 4$, so the length of each edge of the larger cube is $4 \mathrm{~cm}$.

The smaller cube has edges that are half the length of the edges of the larger cube, or $2 \mathrm{~cm}$. The volume of the smaller cube is $2 \times 2 \times 2=8 \mathrm{~cm}^{3}$.

ANsWeR: (C)