Answer:
Option B
\(100\ m^{2}\)
Step-by-step explanation:
Step 1
Find the scale factor
Let
z-----> scale factor
x-----> the volume of the larger solid
y-----> the volume of the smaller solid
we know that
The scale factor elevated to the cube is equal to the volume of the larger solid divided by the volume of the smaller solid
so
\(z^{3}=\frac{x}{y}\)
In this problem we have
\(x=729\ m^{3}, y=125\ m^{3}\)
substitute
\(z^{3}=\frac{729}{125}\)
\(z^{3}=5.832\)
\(z=1.8\) ------> scale factor
Step 2
Find the surface area of the smaller solid
Let
z-----> scale factor
L-----> the surface area of the larger solid
S-----> the surface area of the smaller solid
we know that
The scale factor squared is equal to the surface area of the larger solid divided by the surface area of the smaller solid
so
\(z^{2}=\frac{L}{S}\)
In this problem we have
\(z=1.8, L=324\ m^{2}\)
Substitute and solve for S
\(S=\frac{L}{z^{2}}\)
\(S=\frac{324}{1.8^{2}}\)
\(S=100\ m^{2}\)
