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AP EAMCET202123 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

The volume of a spherical ball is increasing at a rate of 4 cm ^3 ~s ⁻¹ . The rate at which its radius increases, when its volume is 288 cm ^3 , is....... cm s ⁻¹

Options

  1. A1 6
  2. B1 36
  3. C1 9
  4. D1 24

Correct answer

B. 1 36

Step-by-step solution

Given, d v d t =4 cm ^3 / s ...(i) To find, r / d t= ? When, V=288 cm ^3 Let r be the radius of spherical ball Volume (V)= 4 3 r^3 On differentiating w.r.t. t , d V d t = 4 3 3 r^2 d r d t 4 = 12 3 r^2 d r d t 1 r^2 = d r d t ...(ii) When, V=288 288 = 4 3 r^3=r^3=72 3=216 r= [3] 216 =6 ~cm From Eq. (ii), we get d r d t = 1 r^2 = 1 6^2 = 1 36

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