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AP EAMCET202017 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

The sides of an equilateral triangle are increasing at the rate of (2 ~cm ~s ⁻¹ ). How fast does its area increase when its side is (10 ~cm ) ?

Options

  1. A(10 3 ~cm ^2, ~s ⁻¹ )
  2. B(5 3 ~cm ^2, ~s ⁻¹ )
  3. C( 3 ~cm ^2, ~s ⁻¹ )
  4. D(2 3 ~cm ^2, ~s ⁻¹ )

Correct answer

A. (10 3 ~cm ^2, ~s ⁻¹ )

Step-by-step solution

Area of an equilateral triangle is, (A= 3 a^2 4 ) Differentiating with respect to time we get, ( d A d t = 3 4 2 a d a d t ) Here, ( d a d t =2 ~cm ⁻¹ ) when (a=10 ~cm ) So, ( . d A d t |_ a=10 ~cm = 3 4 2 10 2 ) (=10 3 ~cm ^2 s ⁻¹ )

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