Answer:
The correct answer is B. 240.80 inches²
Step-by-step explanation:
The volume scale factor will be given by :
[tex]=\frac{\text{Volume of larger solid}}{\text{Volume of smaller solid}}\\\\=\frac{729}{125}[/tex]
[tex]\text{But, linear scale factor = }\text{(volume scale factor)}^{\frac{1}{3}}[/tex]
[tex]\text{Thus the linear scale factor will be : }(\frac{729}{125})^{\frac{1}{3}}= \frac{9}{5}[/tex]
Also, Area scale factor will be given by :
Area scale factor = (linear scale factor)²
[tex](\frac{9}{5})^2\\\\=\frac{81}{25}[/tex]
Let the area of the larger solid be A
The area of the larger solid will be given by :
[tex]\frac{A}{74.32}=\frac{81}{25}\\\\\implies A = \frac{74.32\times 81}{25}\\\\ \implies A = 240.80[/tex]
Hence, Area of the larger solid = 240.80 inches²
Therefore, The correct answer is B. 240.80 inches²
