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Wittaler [7]
4 years ago
13

The volumes of two similar solids are 1,728 m3 and 343 m3. the surface area of the larger solid is 576 m2. what is the surface a

rea of the smaller solid?
Physics
2 answers:
spayn [35]4 years ago
8 0

I just took this test, the answer is 196 m^2, I got it right


ahrayia [7]4 years ago
3 0
<h2>Answer:</h2>

The surface area of smaller solid is:

                        196 m^2

<h2>Step-by-step explanation:</h2>

We know that for two similar solids:

One with surface area S and Volume V and the other with surface area S' and Volume V' is related by the formula as:

           \sqrt{\dfrac{S}{S'}}=(\dfrac{V}{V'})^\dfrac{1}{3}

We have:

S=576 m^2

V=1728 m^3 and V'=343 m^3

Hence, the equation is written as:

\dfrac{\sqrt{576}}{\sqrt{S'}}=(\dfrac{1728}{343})^{\dfrac{1}{3}}\\\\\\\dfrac{24}{\sqrt{S'}}=(\dfrac{12}{7})^(3\times \frac{1}{3})\\\\\\\dfrac{24}{\sqrt{S'}}=\dfrac{12}{7}\\\\\\\sqrt{S'}=14\\\\\\S'=196

  Hence, the surface area of smaller solid is:

                     196 m^2

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