Answer:
Option a. 196 m²
Step-by-step explanation:
Volumes of two similar solids are 1728 m³ and 343 m³
So the ratio of these volumes = \(\frac{343}{1728}\)
Now we know volume is a three dimensional unit so we find the cube root of the ratio of the volumes to find the ratio of sides.
Scale factor = \(\sqrt[3]{\frac{343}{1728} }=\frac{7}{12}\)
Now we know area of solids is a two dimensional unit so we will square the scale factor and this will be the ratio of area
(Scale factor)² = \((\frac{7}{12})^{2}\) = (Surface area of smaller solid)/(surface area of larger solid)
Area of larger solid = 576 m²
\((\frac{7}{12})^{2}=\frac{S}{576}\)
\(S=\frac{49}{144}.(576)=(49).(4)=196\)
Surface area of of the smaller solid = 196 m²
Option A. is the answer.
