The areas of three adjacent faces of a cuboid | vedclass

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(B) Let the dimensions of the cuboid be $l, b,$ and $h.$The volume of the cuboid is given by $V = l 	imes b 	imes h.$The areas of the three adjacent

Vedclass · Accepted Answer

$V^{2}=xyz$

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(B) Let the dimensions of the cuboid be $l, b,$ and $h.$The volume of the cuboid is given by $V = l 	imes b 	imes h.$The areas of the three adjacent faces are given as:$x = l 	imes b$$y = b 	imes h$$z = h 	imes l$Multiplying these three areas together,we get:$x 	imes y 	imes z = (l 	imes b) 	imes (b 	imes h) 	imes (h 	imes l)$$xyz = l^{2} 	imes b^{2} 	imes h^{2}$$xyz = (l 	imes b 	imes h)^{2}$Since $V = l 	imes b 	imes h$,substituting $V$ into the equation gives:$xyz = V^{2}$Therefore,$V^{2} = xyz$.

The areas of three adjacent faces of a cuboid are $x, y$ and $z.$ If its volume is $V$,then which is true?

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