Respuesta :
[tex]\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{cccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\\\\\
-----------------------------\\\\
\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{s}{s}\implies \cfrac{\sqrt[3]{210}}{\sqrt[3]{1680}}=\cfrac{\sqrt{A}}{\sqrt{856}}[/tex]
solve for A
solve for A
Answer:
The surface area of smaller solid is:
214 m²
Step-by-step explanation:
Let A,V be the surface area and the volume of larger solid.
and A',V' be the surface area and volume of other solid.
We know that the ratio of volume to the surface area of the solid is given by:
[tex]\dfrac{\sqrt{A}}{\sqrt{A'}}=\dfrac{\sqrt[3]{V}}{\sqrt[3]{V'}}[/tex]
On taking power 6 on both side we obtain:
[tex]\dfrac{A^3}{A'^3}=\dfrac{V^2}{V'^2}[/tex]
We have:
V=210 m³ , V'=1680 m³
A=856 m²
Hence, we have:
[tex]\dfrac{(856)^3}{A'^3}=\dfrac{(210)^2}{(1680)^2}\\\\\\A'^3=(107\times 2)^3\\\\\\A'=214\ m^2[/tex]
Hence, the surface area of solid is:
214 m²
