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If the surface area of the cube is changing at a rate of 6m2/s find the rate of change of body diagonal atthe instant when side length is 0.5 m

If the surface area of the cube is changing at a rate of 6m2/s find the rate of change of body diagonal atthe instant when side length
is 0.5 m

Grade:11

1 Answers

Arun
25750 Points
5 years ago
 
Surface area of cube = 6*a^2 where a is its side.
Now given,
dS/dt = 6 m/s^2
thus,
dS/dt = 12*a*da/dt = 6
da/dt = 6/12............................(1)
 
Now relan. b/w body diagonal and length is:
l = a*root3
dl/dt = root3 * da/dt............(2)
from eqns. (1) and (2)
dl/dt = root3 * 6/12 = > root3/2.

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