Question

Plz solve this for me
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Answer 1

Dimensions of a Cubiod :

Length = l, breadth = b , height = h

/* According to the problem given */

1. ) Surface Area = 288 cm²

=> 2(lb+bh+hl) = 288 ---(1)

2 ) Diagonal (d) = 12 cm

$\implies \sqrt{l^{2} + b^{2} + h^{2}} = 12$

$\implies l^{2} + b^{2} + h^{2} = 144 \: --(2)$

$We \:know \:that ,\\(l+b+h)^{2} = l^{2} + b^{2} + h^{2} +2(lb+bh+lh)$

$= 144 + 288\: [ From \: (1) \: and \:(2) ]$

$= 432$

$\implies l + b + h = \sqrt{432} \\= 12\sqrt{3}\:--(3)$

$Here, l + b + h = 4\sqrt{3} + 4\sqrt{3} + 4\sqrt{3}$

$l = b = h = 4\sqrt{3} \:cm$

we conclude that it is a cube .

$Volume \:of \:the \: cube = (side)^{3} \\= (4\sqrt{3} )^{3} \\= 576\sqrt{3} \:cm^{3}$

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