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CBSE Class 9 Answered

if A,B and C denotes the area of three adjescent faces of a cuboid, then find its volume in terms of A,B and C
Asked by Jacques | 02 Mar, 2017, 08:02: PM
answered-by-expert Expert Answer

begin mathsize 16px style Let space the space sides space of space the space cuboid space be space straight x comma space straight y space and space straight z. space Given space straight A comma space straight B space and space straight C space are space the space areas space of space three space adjacent space faces space of space the space cuboid. Using space area space of space straight a space square equals left parenthesis side right parenthesis squared comma space we space get Hence comma space straight A equals xy comma space space straight B equals yz comma space straight C equals xz rightwards double arrow ABC equals space left parenthesis xy right parenthesis left parenthesis yz right parenthesis left parenthesis xz right parenthesis space rightwards double arrow ABC equals straight x squared straight y squared straight z squared Squaring space both space sides comma space we space get rightwards double arrow square root of ABC equals xyz Now comma space volume space of space the space cuboid space equals space xyz Thus comma space the space volume space of space cuboid comma space straight V equals space xyz equals square root of ABC. end style

Answered by | 03 Mar, 2017, 05:50: PM

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