Archive
3rd of March 2017
Mathematics
Q:

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

Jacques Johnson - CBSE - Class IX

Thursday, March 02, 2017 at 20:02:PM

A:

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

Friday, March 03, 2017 at 17:50:PM