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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

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

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Surface area of cube = 6*a^2 where a is its side.
Now given,
dS/dt = 5 m/s^2
thus,
dS/dt = 12*a*da/dt = 5
da/dt = 5/12............................(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 * 5/12 = > 5root3/12.

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