The surface area of a cube is #486# #i##n^2#. What is the volume of the cube?

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Answer 1 · 2017-02-20T21:57:44

Volume is #729 " in"^3#.

The surface of a cube is given by the expression:

#S = 6 L^2#,

were #L# is the length of the edge of the cube.

On the other hand, the volume of a cube is obtained from formula

#V = L^3#.

Therefore, clearing #L# of the first formula and substituting the value obtained in the second, we will have:

#S = 6 L^2 rArr L = sqrt {S/6} rArr V = (sqrt {S/6})^3 = (sqrt {486/6} )^3 = 729 " in"^3#