The volumes of two similar solids are 210 m3 and 1,680 m3. The surface area of the larger solid is 856 m2. What is the surface a

Question

Elodia

1 month ago

5

The volumes of two similar solids are 210 m3 and 1,680 m3. The surface area of the larger solid is 856 m2. What is the surface a

rea of the smaller solid?

Mathematics

3 answers:

lawyer [12.5K] · Answer 1 · 2026-03-30T21:11:15+03:00

lawyer [12.5K]1 month ago

6 0

We understand that

$scale \ factor^{3}=\frac {volume\ larger\ solid }{volume\ smaller\ solid}$

thus

Determine the scale factor

$volume\ larger\ solid= 1,680\ m^{3} \\ volume\ smaller\ solid= 210\ m^{3}$

substitute the values into the formula

$scale \ factor^{3}=\frac {1,680 }{210}$

$scale \ factor^{3}=8$

$scale \ factor=\sqrt[3]{8} \\ scale \ factor= 2$

Find the smaller solid's surface area

we understand that

$scale \ factor^{2}=\frac {surface\ area\ larger\ solid }{surface\ area\ smaller\ solid}$

$surface\ area\ larger\ solid =856\ m^{2} \\ scale\ factor =2$

$surface\ area\ smaller\ solid= \frac{surface\ area\ larger\ solid}{scale \ factor^{2}}$

substituting the values

$surface\ area\ smaller\ solid= \frac{856}{2^{2}}$

$surface\ area\ smaller\ solid=214\ m^{2} }$

therefore

the answer yields

The surface area of the smaller solid computes to $214\ m^{2}$

tester [12.3K] · Answer 2 · 2026-03-30T21:14:36+03:00

tester [12.3K]1 month ago

4 0

$\bf \textit{ratio relations}\\
\begin{array}{llll}
sides&\cfrac{s}{s}\\\\
Area&\cfrac{s^2}{s^2}\\\\
Volume&\cfrac{s^3}{s^3}
\end{array}\qquad thus\\\\
-----------------------------\\\\
\cfrac{\textit{smaller volume}}{\textit{bigger volume}}\implies \cfrac{210}{1680}=\cfrac{s^3}{s^3}\implies \cfrac{210}{1680}=\left( \cfrac{s}{s} \right)^3
\\\\\\
\sqrt[3]{\cfrac{210}{1680}}=\cfrac{s}{s}\implies \cfrac{\sqrt[3]{210}}{\sqrt[3]{1680}}=\cfrac{s}{s}\\\\
-----------------------------\\\\

$

$\bf now
\\\\
\cfrac{\textit{smaller area}}{\textit{bigger area}}\implies \cfrac{A}{856}=\cfrac{s^2}{s^2}\implies \cfrac{A}{856}=\left( \cfrac{s}{s}\right)^2
\\\\\\\\
\textit{however, recall that }\sqrt[3]{\cfrac{210}{1680}}=\cfrac{s}{s}\qquad thus
\\\\\\\\
\cfrac{A}{856}=\left( \sqrt[3]{\cfrac{210}{1680}}\right)^2\implies 
\cfrac{A}{856}=\cfrac{\sqrt[3]{210^2}}{\sqrt[3]{1680^2}}$

Resolve for "A" to determine the surface area of the smaller solid.