15. The volume of a cube is $V \mathrm{~cm}^{3}$. The surface area of the cube is $2 V \mathrm{~cm}^{2}$. What is the value of $V$ ?
A 8
B 16
C 27
D 64
E 128
Solution
C

Let the side-length of the cube be $x \mathrm{~cm}$. Since the volume is $V \mathrm{~cm}^{3}$, we have $V=x^{3}$. Also, since the area of one face of the cube is $x^{2} \mathrm{~cm}^{2}$ and the total surface area of the cube is $2 V \mathrm{~cm}^{2}$, we have $2 V=6 x^{2}$. Therefore $2 x^{3}=6 x^{2}$ and hence $x=0$ or $2 x=6$. Therefore $x=3$ and hence $V=3^{3}=27$.