Measure-of-the-side-of-a-cube-is-double-of-the-the-side-of-the-cube-inside-it-What-is-empty-space-in-larger-cube-

Question Number 5533 by Rasheed Soomro last updated on 18/May/16

$$\mathrm{Measure}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{double} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{inside}\:\mathrm{it}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{empty}\:\mathrm{space}\:\mathrm{in}\:\mathrm{larger}\:\mathrm{cube}? \\ $$

Commented by FilupSmith last updated on 18/May/16

Empty space is equal to the larger cube subtract the smaller. V_(small) =x^3 V_(double) =(2x)^3 =8x^3 V=8x^3 −x^3 =7x^3

$$\mathrm{Empty}\:\mathrm{space}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{larger} \\ $$$$\mathrm{cube}\:\mathrm{subtract}\:\mathrm{the}\:\mathrm{smaller}. \\ $$$$ \\ $$$${V}_{{small}} ={x}^{\mathrm{3}} \\ $$$${V}_{{double}} =\left(\mathrm{2}{x}\right)^{\mathrm{3}} =\mathrm{8}{x}^{\mathrm{3}} \\ $$$${V}=\mathrm{8}{x}^{\mathrm{3}} −{x}^{\mathrm{3}} =\mathrm{7}{x}^{\mathrm{3}} \\ $$

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