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KCET2017MathematicsProperties of Triangles

The rate of change of volume of a sphere with respect to its surface area when the radius is ( 4 ) ( cm ) is

Options

  1. A( 4 ~cm ³ ~cm -2 )
  2. B( 2 ~cm ³ ~cm ⁻² )
  3. C( 6 ~cm ³ ~cm ⁻² )
  4. D( 8 ~cm ³ ~cm ⁻² )

Correct answer

B. ( 2 ~cm ³ ~cm ⁻² )

Step-by-step solution

Given that, radius of the sphere is [ r=4 ] We now that, volume sphere is given by [ V= 4 3 r² (1) ] and surface area of sphere is given by [ S=4 r² (2) ] Differentiating Eqs. (1) and (2) with respect to ( r ), we get [ d V d r = 4 3 3 r²=4 r² ] [ array l And d S d r =4 2 r=8 r So, d V d S = d V / d r d S / d r = [ 4 m r² 8 r ]= r 2 At r=4 ~cm , we get ( r 2 )_ r=4 = 4 2 =2 ~cm ³ ~cm ⁻² array ]

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