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  • The density of a certain metal is . If a cube of this metal

The density of a certain metal is \mathrm{10.5 \ g/cm^3}. If a cube of this metal weighs \mathrm{630 \ g}, what is the length of one side of the cube?

Option: 1

\mathrm{3 \ cm}


Option: 2

\mathrm{4 \ cm}
 


Option: 3

\mathrm{5 \ cm}

 


Option: 4

\mathrm{6 \ cm}


Answers (1)

best_answer

Correct option 2) 4 cm

The volume of the cube is equal to the length of one side cubed. Therefore, the volume of the cube is \mathrm{(4\ cm)^3=64\ cm^3}. Since the density of the metal is \mathrm{10.5 \ g/cm^3}, the mass of the cube can be calculated as \mathrm{10.5 \ g/cm^3 \times 64 \ cm^3 = 672 \ g}. But we know that the actual weight of the cube is \mathrm{630 \ g}. So, we can calculate the actual volume of the cube as \mathrm{630 \ g / 10.5 \ g/cm^3 = 60 \ cm^3}. Thus, the length of one side of the cube is \mathrm{\sqrt[3]{60\ cm^3}\approx4\ cm}.

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manish

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