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Question Number 26461 by ajfour last updated on 25/Dec/17

Commented by ajfour last updated on 25/Dec/17

A layer is cut from the back of   upper large cuboid (of front   surface area p and volume −q ).  This layer is of volume x^3 , where  x is the remaining thickness.  From the upper remaining layer  of thickness x three cuboids of  front area p/3  can be formed  whose length v minus width u  is equal to the thickness x .  Evaluate  x in terms of p, q .

$${A}\:{layer}\:{is}\:{cut}\:{from}\:{the}\:{back}\:{of}\: \\ $$$${upper}\:{large}\:{cuboid}\:\left({of}\:{front}\:\right. \\ $$$$\left.{surface}\:{area}\:\boldsymbol{{p}}\:{and}\:{volume}\:−\boldsymbol{{q}}\:\right). \\ $$$${This}\:{layer}\:{is}\:{of}\:{volume}\:\boldsymbol{{x}}^{\mathrm{3}} ,\:{where} \\ $$$${x}\:{is}\:{the}\:{remaining}\:{thickness}. \\ $$$${From}\:{the}\:{upper}\:{remaining}\:{layer} \\ $$$${of}\:{thickness}\:\boldsymbol{{x}}\:{three}\:{cuboids}\:{of} \\ $$$${front}\:{area}\:\boldsymbol{{p}}/\mathrm{3}\:\:{can}\:{be}\:{formed} \\ $$$${whose}\:{length}\:\boldsymbol{{v}}\:{minus}\:{width}\:\boldsymbol{{u}} \\ $$$${is}\:{equal}\:{to}\:{the}\:{thickness}\:\boldsymbol{{x}}\:. \\ $$$${Evaluate}\:\:\boldsymbol{{x}}\:{in}\:{terms}\:{of}\:{p},\:{q}\:. \\ $$

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