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Solution for 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 (A) λ % (B) 2 λ % (C) 3 λ % (D) None of These - CBSE (Science) Class 12 - Mathematics

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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
(a) λ %
(b) 2 λ %
(c) 3 λ %
(d) none of these

Solution

(c) 3 λ %

Let the radius of the cone be x, the height be 2x and the volume be y.

\[\frac{∆ x}{x} = \lambda % \]

\[ \Rightarrow y = \frac{1}{3}\pi x^2 \times 2x = \frac{2}{3}\pi x^3 \]

\[ \Rightarrow \frac{dy}{dx} = 2\pi x^2 \]

\[ \Rightarrow \frac{∆ y}{y} = \frac{2\pi x^2}{y}dx = \frac{3}{x} \times \lambda x\]

\[ \Rightarrow \frac{∆ y}{y} = 3\lambda\%\]

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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 (A) λ % (B) 2 λ % (C) 3 λ % (D) None of These Concept: Approximations.
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