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