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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

#### 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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#### APPEARS IN

RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 8 | Page no. 13

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Solution for 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 concept: Approximations. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
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