Cubes - diff

Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.

Result

a =  10 cm
b =  12 cm

Solution:

(a+2)3−a3=728 (a+2)(a2+4a+4)−a3=728 6a2+12a+8=728 a1,2=−q±D2p=−12±1742412 a1,2=−12±13212 a1,2=−1±11 a1=10 a2=−12 a>0 a=10 b=a+2=12(a+2)^3-a^3 = 728 \ \\ (a+2)(a^2+4a+4) -a^3 = 728 \ \\ 6a^2 + 12a +8 = 728 \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -12 \pm \sqrt{ 17424 } }{ 12 } \ \\ a_{1,2} = \dfrac{ -12 \pm 132 }{ 12 } \ \\ a_{1,2} = -1 \pm 11 \ \\ a_{1} = 10 \ \\ a_{2} = -12 \ \\ a>0 \ \\ a = 10 \ \\ b = a+2 = 12

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