The surface area of smaller solid is:
196 m^2
We know that for two similar solids:
One with surface area S and Volume V and the other with surface area S' and Volume V' is related by the formula as:
[tex]\sqrt{\dfrac{S}{S'}}=(\dfrac{V}{V'})^\dfrac{1}{3}[/tex]
We have:
S=576 m^2
V=1728 m^3 and V'=343 m^3
Hence, the equation is written as:
[tex]\dfrac{\sqrt{576}}{\sqrt{S'}}=(\dfrac{1728}{343})^{\dfrac{1}{3}}\\\\\\\dfrac{24}{\sqrt{S'}}=(\dfrac{12}{7})^(3\times \frac{1}{3})\\\\\\\dfrac{24}{\sqrt{S'}}=\dfrac{12}{7}\\\\\\\sqrt{S'}=14\\\\\\S'=196[/tex]
Hence, the surface area of smaller solid is:
196 m^2
