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

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

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Answer 1 · 2017-02-20T21:57:44

Volume is $729 {in}^{3}$ $729 " in"^3$ .

Explanation:

The surface of a cube is given by the expression:

$S = 6 L^{2}$ $S = 6 L^2$ ,

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

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

$V = L^{3}$ $V = L^3$ .

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

$S = 6 L^{2} \Rightarrow L = \sqrt{\frac{S}{6}} \Rightarrow V = {(\sqrt{\frac{S}{6}})}^{3} = {(\sqrt{\frac{486}{6}})}^{3} = 729 {in}^{3}$ $S = 6 L^2 rArr L = sqrt {S/6} rArr V = (sqrt {S/6})^3 = (sqrt {486/6} )^3 = 729 " in"^3$

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

1 Answer

Explanation:

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