we know that
\(scale \ factor^{3}=\frac {volume\ larger\ solid }{volume\ smaller\ solid}\)
so
Find the value of the scale factor
\(volume\ larger\ solid= 1,680\ m^{3} \\ volume\ smaller\ solid= 210\ m^{3}\)
substitute the values in the formula
\(scale \ factor^{3}=\frac {1,680 }{210}\)
\(scale \ factor^{3}=8\)
\(scale \ factor=\sqrt[3]{8} \\ scale \ factor= 2\)
Find the surface area of the smaller solid
we know that
\(scale \ factor^{2}=\frac {surface\ area\ larger\ solid }{surface\ area\ smaller\ solid}\)
\(surface\ area\ larger\ solid =856\ m^{2} \\ scale\ factor =2\)
\(surface\ area\ smaller\ solid= \frac{surface\ area\ larger\ solid}{scale \ factor^{2}}\)
substitute the values
\(surface\ area\ smaller\ solid= \frac{856}{2^{2}}\)
\(surface\ area\ smaller\ solid=214\ m^{2} }\)
therefore
the answer is
The surface area of the smaller solid is equal to \(214\ m^{2}\)
