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  # If the Ratio of Base Radius and Height of a Cone is 1 : 2 and Percentage Error in Radius is λ %, Then the Error in Its Volume is - CBSE (Science) Class 12 - Mathematics
  
  #### Question
  
  If the ratio of base radius and height of a cone is 1 : 2 and percentage error in radius is λ %, then the error in its volume is
  
  • λ %
  
  • 2 λ %
  
  • 3 λ %
  
  • none of these
  
  #### Solution
  
  3 λ %
  
  Let the radius of the cone be x, the height be 2x and the volume be y.
  
  $\frac{∆ x}{x} = \lambda$ %
  
  $\Rightarrow y = \frac{1}{3}\pi x^2 \times 2x = \frac{2}{3}\pi x^3$
  
  $\Rightarrow \frac{dy}{dx} = 2\pi x^2$
  
  $\Rightarrow \frac{∆ y}{y} = \frac{2\pi x^2}{y}dx = \frac{3}{x} \times \lambda x$
  
  $\Rightarrow \frac{∆ y}{y} = 3\lambda\%$
  
  Is there an error in this question or solution?
  
  #### Video TutorialsVIEW ALL [2]
  
  Solution If the Ratio of Base Radius and Height of a Cone is 1 : 2 and Percentage Error in Radius is λ %, Then the Error in Its Volume is Concept: Approximations.
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