Question

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 area of the smaller solid? 107 m2 214 m2 1034 m2 6848 m2

Answer 1

The surface area of the smaller solid is found to be 214 square meters.

What is Surface area?

The surface area is given as the sum of the area of all the faces of a three-dimensional object.

The same shape has equivalent ratio of the surface area to volume. It is given as:

$\rm \dfrac{\sqrt{area_1}}{\sqrt{area_2}}=\dfrac{\sqrt[3]{Volume_1} }{\sqrt[3]{Volume_2} }$

On considering the power of 6 at both the sides of the equation:

$\rm \dfrac{area_1^2}{area_2^2}=\dfrac{volume_1}{volume_2}$

Considering area 1 and volume 1 for the larger solid, and area 2 and volume 2 for the smaller solid, substituting the values give:

$\rm\dfrac{(856\;m^2)^3}{(area_^2)^3}=\dfrac{(1680\;m^3)^2}{(210\;m^3)^2}$

By solving the above equation, the area of the smaller solid is found as 214 square meters. Thus, option B is correct.

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