Question 967015
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 {{{1+6=7}}} cubes.
{{{875/7=125}}} , so if the solid volume is {{{875cm^3}}} ,
the volume of the each cube (the original cube and the other 6 identical ones) is
{{{125cm^3}}} .
Since the volume of a cube is the cube of the edge length,
the length of the edge of those cubes, in cm, is {{{root(3,125)=5}}} .
The surface area of a face of a cube with edge length {{{5cm}}} is
{{{(5cm)(5cm)=25cm^2}}} .
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 {{{6-1=5}}} exposed faces.
The total exposed surface of the 7-cube cluster consists of
{{{6*5=30}}} cube faces (5 faces from each of 6 cubes).
So the total surface area is {{{30*25cm^2=highlight(750)cm^2}}}