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BITSAT2010MathematicsApplication of DerivativesActual

If a circular plate is heated uniformly, its area expands (3 c ) times as fast as its radius, then the value of (c ) when the radius is 6 units, is

Options

  1. A(4 )
  2. B(2 )
  3. C(6 )
  4. D(3 )

Correct answer

A. (4 )

Step-by-step solution

Let (A ) sq. units in the area measure when the radius is (r ) units. their (A= r^2 ) Differentiate both side w.r.t ' (t ) ' ( d A d t =2 r d r d t ) ...(i)) We have, ( d A d t =3 c d r d t ) From eqn (i), we get (3 c d r d t =2 r d r d t 3 c=2 r ) Now, (c= 2 3 (6)=4 ) when (r=6 )

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