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

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KollegeApply · Accepted Answer

3 λ % Let the radius of the cone be x, the height be 2x and the volume be y. ∆ x/x = \lambda % \Rightarrow y = $\frac{1}{3}$$\pi$ x^2 $\times$ 2x = $\frac{2}{3}$$\pi$ x^3 \Rightarrow dy/dx = 2$\pi$ x^2 \Rightarrow ∆ y/y = 2$\pi$ x^2/ydx = 3/x $\times$ \lambda x \Rightarrow ∆ y/y = 3\lambda\%

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