SOLUTION: One cube has each of its faces covered by one face of an identical cube, making a solif as shown. The volume of the solid is 875 cm cubed. What, in cm squared, is the surface ar

Question 967015: One cube has each of its faces covered by one face of an identical cube, making a solif as shown. The volume of the solid is 875 cm cubed.
What, in cm squared, is the surface area of the solid?
A 750
B 800
C 875
D 900
E 1050
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The solid is not shown, but anyone who ever rolled dice knows that a cube has 6 faces,
so attaching one cube to each face of the original cube,
we end up with a cluster of cubes.
, so if the solid volume is ,
the volume of the each cube (the original cube and the other 6 identical ones) is
.
Since the volume of a cube is the cube of the edge length,
the length of the edge of those cubes, in cm, is .
The surface area of a face of a cube with edge length is
.
In the 7 cube cluster, none of the 6 faces of the original cube is visible (all are covered).
The other 6 identical cubes attached to the original cube have one face covered (attached to the original cube,
so each one has exposed faces.
The total exposed surface of the 7-cube cluster consists of
cube faces (5 faces from each of 6 cubes).
So the total surface area is
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