Sum of the length,width and depth of a cuboid | vedclass

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(C) Let the length,width,and depth of the cuboid be $l$,$b$,and $h$ respectively.Given that the sum of dimensions is $l + b + h = s$.The diagonal of t

Vedclass · Accepted Answer

$s^{2}-d^{2}$

Vedclass · Answer

(C) Let the length,width,and depth of the cuboid be $l$,$b$,and $h$ respectively.Given that the sum of dimensions is $l + b + h = s$.The diagonal of the cuboid is given by $\sqrt{l^{2} + b^{2} + h^{2}} = d$,which implies $l^{2} + b^{2} + h^{2} = d^{2}$.We know the algebraic identity: $(l + b + h)^{2} = l^{2} + b^{2} + h^{2} + 2(lb + bh + hl)$.Substituting the given values,we get: $s^{2} = d^{2} + 2(lb + bh + hl)$.The surface area of a cuboid is given by $2(lb + bh + hl)$.Therefore,$2(lb + bh + hl) = s^{2} - d^{2}$.Thus,the surface area is $s^{2} - d^{2}$.

Sum of the length,width and depth of a cuboid is $s$ and its diagonal is $d$. Its surface area is

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