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COMEDK2024Evening ShiftMathematicsApplication of DerivativesActual

The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is

Options

  1. A2 : 3
  2. B3: 2
  3. C3:
  4. D: 6

Correct answer

C. 3:

Step-by-step solution

Let the side of the cube be a and the radius of the sphere be r . Given that the side of the cube is equal to the diameter of the sphere, we have a = 2r . Let the rate of increase of the side and the radius be da dt = dr dt = k . The surface area of the cube is S_c = 6a^2 . The rate of increase of the surface area of the cube is dS_c dt = 12a da dt = 12(2r)k = 24rk . The surface area of the sphere is S_s = 4 r^2 . The rate of increase of the surface area of the sphere is dS_s dt = 8 r dr dt = 8 rk . The ratio of th

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