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If surface area of a cube is changing at a rate of 5m^2/s,find the rate of change of body diagonal at the moment when side length is 1m
Surface area of cube = 6*a^2 where a is its side.Now given,dS/dt = 5 m/s^2thus,dS/dt = 12*a*da/dt = 5da/dt = 5/12............................(1) Now relan. b/w body diagonal and length is:l = a*root3dl/dt = root3 * da/dt............(2)from eqns. (1) and (2)dl/dt = root3 * 5/12 = > 5root3/12.
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