The edges of three of the four cubes are 1, c | vedclass

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(B) Let the edge of the fourth cube be $x\, cm$.The volume of a cube with edge $a$ is given by $V = a^3$.The volumes of the given cubes are $1^3 = 1\,

Vedclass · Accepted Answer

$12$

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(B) Let the edge of the fourth cube be $x\, cm$.The volume of a cube with edge $a$ is given by $V = a^3$.The volumes of the given cubes are $1^3 = 1\, cm^3$,$9^3 = 729\, cm^3$,and $10^3 = 1000\, cm^3$.According to the problem,the sum of the volumes of the cubes with edges $9\, cm$ and $10\, cm$ is equal to the sum of the volumes of the cubes with edges $1\, cm$ and $x\, cm$.So,$9^3 + 10^3 = 1^3 + x^3$.$729 + 1000 = 1 + x^3$.$1729 = 1 + x^3$.$x^3 = 1728$.Taking the cube root on both sides,$x = \sqrt[3]{1728} = 12\, cm$.Thus,the edge of the fourth cube is $12\, cm$.

The edges of three of the four cubes are $1\, cm, 9\, cm$ and $10\, cm$ respectively. If the total volume of two cubes with $9\, cm$ edge and $10\, cm$ edge is equal to the volume of the remaining two cubes,find the edge of the fourth cube in $cm$.

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