We can use the fact that the ratios of corresponding lengths, areas, and volumes of similar solids are equal. Let's denote the surface area of the larger solid with $A$. We have:
$$\frac{\text{surface area of smaller solid}}{\text{surface area of larger solid}}=\frac{108}{A}$$
Since the solids are similar, their volumes are in the same ratio as the cubes of their corresponding side lengths. Let's denote the side lengths of the smaller solid with $x$, then the side length of the larger solid is $\frac{x}{\sqrt[3]{\frac{857.5}{540}}}$. We have:
$$\frac{\text{volume of smaller solid}}{\text{volume of larger solid}}=\left(\frac{x}{\frac{x}{\sqrt[3]{\frac{857.5}{540}}}}\right)^3=\frac{540}{857.5}$$
Simplifying, we get:
$$\frac{\sqrt[3]{\frac{857.5}{540}}^3}{1}=\frac{\sqrt[3]{857.5}}{\sqrt[3]{540}}=\frac{\sqrt[3]{857.5/540}}{1}$$
Multiplying the two ratios, we obtain:
$$\frac{\text{surface area of smaller solid}}{\text{surface area of larger solid}}\cdot\frac{\text{volume of smaller solid}}{\text{volume of larger solid}}=\frac{108}{A}\cdot\frac{540}{857.5/540}=\frac{108\cdot 540\cdot 540}{857.5}\approx 513.6$$
Setting this equal to the ratio of the surface areas of the similar solids, we get:
$$\frac{A}{108}=\frac{857.5}{540}\cdot\frac{1}{\frac{108\cdot 540\cdot 540}{857.5}}\approx 0.45195$$
Therefore, $A\approx 0.45195\cdot 108\approx\boxed{48.84\text{ mm}^2}$, which is closest to answer choice $\textbf{(A)}$.
The values of two similar solids are 857.5 mm cubed and 540 mm cubed the surface area of the smaller solid is 108 mm squared what is the surface area of the larger solid
A 147 mm2
B 68mm2
C. 16mm2
D. 216 mm2
3 answers
See my correct solution above this one.
Nobody can read the bot's solution, besides that, its solution is totally bogus
Nobody can read the bot's solution, besides that, its solution is totally bogus
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