5. Two similar figures have volumes 27 in.? and 125 in.?. The surface area of the smaller figure is 63 in.. (1 point)Find the surface area of the larger figure.O105 in.?О 136 in.?О 175 in.?О292in 2

Answer:[tex]175\ in^{2}[/tex] Step-by-step explanation:step 1Find the scale factor we know that If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube Let z----> the scale factor x----> volume of the larger solid y----> volume of the smaller solid [tex]z^{3}=\frac{x}{y}[/tex] we have [tex]x=125\ in^{3}[/tex] [tex]y=27\ in^{3}[/tex] substitute[tex]z^{3}=\frac{125}{27}[/tex] [tex]z=\frac{5}{3}[/tex] step 2Find the surface area of the larger solidwe know that If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared Let z----> the scale factor x----> surface area of the larger solid y----> surface area of the smaller solid [tex]z^{2}=\frac{x}{y}[/tex] we have [tex]z=\frac{5}{3}[/tex] [tex]y=63\ in^{2}[/tex] substitute [tex](\frac{5}{3})^{2}=\frac{x}{63}[/tex] [tex]x=\frac{25}{9}*63=175\ in^{2}[/tex]