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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 - 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

##### Options
• 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.

$\frac{∆ x}{x} = \lambda$ %

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

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

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

$\Rightarrow \frac{∆ y}{y} = 3\lambda\%$

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