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Question

(B) The volume of a cube with side $a$ is given by $V = a^3$.The volumes of the three given cubes are:$V_1 = (6\, cm)^3 = 216\, cm^3$$V_2 = (8\, cm)^3

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) The volume of a cube with side $a$ is given by $V = a^3$.The volumes of the three given cubes are:$V_1 = (6\, cm)^3 = 216\, cm^3$$V_2 = (8\, cm)^3 = 512\, cm^3$$V_3 = (10\, cm)^3 = 1000\, cm^3$When these cubes are melted together,the total volume $V_{total}$ of the new cube is the sum of the individual volumes:$V_{total} = V_1 + V_2 + V_3 = 216 + 512 + 1000 = 1728\, cm^3$Let the side of the new cube be $a$. Then:$a^3 = 1728$$a = \sqrt[3]{1728}$$a = 12\, cm$Thus,the side of the resulting cube is $12\, cm$.

Three metal cubes with edges $6\, cm$,$8\, cm$,and $10\, cm$ respectively are melted together and formed into a single cube. Find the side of the resulting cube (in $cm$).

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