20. One cube has each of its faces covered by one face of an identical cube, making a solid as shown. The volume of the solid is $875 \mathrm{~cm}^{3}$. What, in $\mathrm{cm}^{2}$, is the surface area of the solid?
A 750
B 800
C 875
D 900
E 1050
Solution: $\mathbf{A}$
The solid is made up of 7 cubes. So each of them has volume $\frac{1}{7}(875)=125=5^{3} \mathrm{~cm}^{3}$. Hence the side length of each of the cubes is $5 \mathrm{~cm}$. Each of the 6 faces of the central cube is covered by one face of one of the other 6 cubes, each of which has 5 faces showing. So the surface of the figure is made up of $6 \times 5=30$ squares, each with side length $5 \mathrm{~cm}$ and hence area $25 \mathrm{~cm}^{2}$. Hence the total area of the figure is $30 \times 25=750 \mathrm{~cm}^{2}$.