Question

the total surface area is of a cube is 54 cm what is the lenght of its
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Answer 1

${\boxed{\sf{T.S.A. \ of \ cube = 6 * (Edge)^2}}}$

$\sf{Let, \ edge \ of \ cube = x \ cm.}$

$\sf{\therefore \quad T.S.A. = 6x^2}$

$\sf{Also, \ T.S.A. \ of \ cube = 54 \ cm^2 \qquad (Given)}$

$\sf{So, \ \implies \ 6x^2 = 54}$

$\sf{Transposing}$

$\sf{\implies \ x^2 = {\dfrac{54}{6}}}$

$\sf{\implies \ x^2 = 9}$

$\sf{\implies x = {\sqrt{9}} }$

$\sf{\implies \ x =}$ ± $\sf{3}$

$\sf{Since, \ edge \ can't \ be \ negative.}$

$\sf{So, \ Edge = 3 \ cm}$

$\sf\red{Edge \ of \ cube \ is \ 3 \ cm.}$