The area of three adjacent faces of a rectang | vedclass

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Question

(B) Let the dimensions (length,width,and height) of the rectangular box be $x, y,$ and $z$ respectively.The areas of the three adjacent faces are give

Vedclass · Accepted Answer

$\sqrt{pqr} \, cm^3$

Vedclass · Answer

(B) Let the dimensions (length,width,and height) of the rectangular box be $x, y,$ and $z$ respectively.The areas of the three adjacent faces are given as:$p = xy$$q = yz$$r = zx$The volume of the rectangular box is $V = xyz$.Multiplying the three areas together,we get:$p 	imes q 	imes r = (xy) 	imes (yz) 	imes (zx)$$pqr = x^2 y^2 z^2$$pqr = (xyz)^2$Taking the square root of both sides:$xyz = \sqrt{pqr}$Therefore,the volume of the box is $\sqrt{pqr} \, cm^3$.

The area of three adjacent faces of a rectangular box are $p, q$ and $r$ square $cm$. The volume of the box is given by

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