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# Solution for If an Error of K% is Made in Measuring the Radius of a Sphere, Then Percentage Error in Its Volume is (A) K% (B) 3k% (C) 2k% (D) K/3% - CBSE (Science) Class 12 - Mathematics

#### Question

If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is
(a) k%
(b) 3k%
(c) 2k%
(d) k/3%

#### Solution

(b) 3k%
Let x be the radius of the sphere and y be its volume.
Then,

$\frac{∆ x}{x} \times 100 = k$

$\text { Also }, y = \frac{4}{3}\pi x^3$

$\Rightarrow \frac{dy}{dx} = 4\pi x^2$

$\Rightarrow \frac{∆ y}{y} = \frac{4\pi x^2}{y}dx = \frac{4\pi x^2}{\frac{4}{3}\pi x^3} \times \frac{kx}{100}$

$\Rightarrow \frac{∆ y}{y} \times 100 = 3k$

$\text { Hence, the error in the volume is } 3k % .$

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Solution If an Error of K% is Made in Measuring the Radius of a Sphere, Then Percentage Error in Its Volume is (A) K% (B) 3k% (C) 2k% (D) K/3% Concept: Approximations.
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